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ELE
J
Go:^vii
J
TH
I
IMUx (^' Co.'s ^bucational Series.
ELEMENTARY HYDROSTATICS
FA'
,
J. HAMBLIN SMITH, M.A.,
GONVILLE AND CAIUS OOLLllGE.. AND LATE LECTURER AT
ST. Peter's college, Cambridge.
J
THIRD CANADIAN COPYRIGHT EDITION.
Authorized by the Minister of Education.
PRICB 73 CENTS.
TORONTO :
ADAM MILLER & CO.,
1879.
Entered acoordir : to Act o. PavUament o, Canada, in the year 1876. by
ADAM MILLER & CO.,
In me Office of the Minister of Agriculture.
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by
PREFACE
The Elements oi Hydrostatics seem capable «jf bein^
presented in a simpler form than that in which they
appear in all the works on the subject \nth which I aai
acquaintpd. I have therefore attempted to give a simple
explanation of the Mathematical Theory of Hydrostatics
H.nd the practical application of it.
Prior to the publication of this work some copies w^ere
privately circulated with a view to obtain opinions from
Teachers of experience as to the sutliciency and accuracy
of the inforaiation contained in it. A few suggestions
received in consequence of this arrangement will be found
in the Notes at ihe end of the volume.
I am indebted to several friends for the collection of
Miscellaneous Examples given in Chapter vill. In
conclusion I have to expiess my thanks for the favour
with which my attemptt^ to simplify the course of Elemen
tary Mathematics have been received by College Tutors
and Masters in Schuols.
J. HAMBLIN SMITH.
Cambridge, 1870.
CONTEXTS
i
..
ClIArTEli I.
ViQS
On Fluid Pkessoue 1
CHAP i'Eli 11.
On the Puessuue of a Fluid aoti;d ox by (Iuavitt . 11
CHAi'TER III.
On Specifio Guavixy 20
CHAPTER iV.
On the Conditions of Equiliiuhum oi' Bodtks undeb tue
Action of Fluids '>!'
CHAPTER V.
On the Propeijties of Air ...««. bw
CHAPTER VI.
On the Application of Air , . • • q • 6G
CiiAPJ ER Vll.
On the Theujiometeu 77
CHAPTER \'III.
Miscellaneous Examples . . . . . • • 83
Answers . ..•••••* ^^
HYDROSTATICS.
CHAPTER I.
On Fluid Pressure,
t
1. Hydrostatics was originally, as the namo imports, the
sciouco which treated of tho P]quilibriiiia of Fluids, or of
bodies in equilibrium mider tho action of forces some of
which arc produced by tho action of fluids. It is now ex
tended so as to include many other theorems relating to the
properties of fluids.
2. A fluid is a substance whose parts yield to any force
impressed on it, avd by yielding are easily moved among
themselves.
3. This definition 8ci)arates fluids from rigid bodies, in
which the particles cannot be moved among each other by any
force, however great, but it does not se)arate fluids from
powders, such as flour, in which wo have a collection of
particles which can bo moved among themselves by tho appli
iiation of a slight force.
4. A fluid difl'ers from a powder in this way : the particles
composing a powder do not move among themselves "withou*
friction, whereas the particles that make up a fluid move one
over another without any friction.
For example, if you empty a mug of flour on a table the
friction between tho particles will soon bring the flour to rest
m more or less of a heap; whereas if you empty a nmg of
water the particles, moving without friction, run in all direc
tions, and the wholo body of vratcr is spread out into a very
fchiu sheet.
a u. 1
aV FLUID PRESSURE.
5. To <listingiiish fluiils tVtuii »ow(lors wo must thoroforo
make nil ail.lili(»ii to Art. J, uiiU \no y;ivo tlio follitviiig a^ a
coinplcto dclinition of a (laid.
l)i;t'. A Jlaid is a ^uhdance vhone jxirlx yield to any f^rco
imprc'sscd on it, and /'// yicldiiKj are Cdsdy mnjed ainnng
Ihetnsclces without /rii'f.ion, and (dso (H't without /fiction on
aiii/ aiir/aco with which they are in contuct.
This dclinition includes nut only tlio bodies to which iu
ordinary convoivsation wo apply the tonns "lliiid"and "liquid,"
such aH watci, oil, .ind mercury, but also such bcilios as air,
gas and steam.
G. Fluids may bo conveniently diviiieil into two chussob,
liquid and (jiiscous. JJy tho tevnj liquid we understand an
incompres.sible and inelastic Ihiid. In reality nil tluids with
which wo are a(.(iuainted aro c<»mpressible, that is, a given
voluii;0 of iluid can by pressure be reduced in volume. Still
80 great a force i.s rccpiired to compress to any a]»prcciablc
extent such lluids as water and mercury, that wo may regard
them as incompressible in treating of tho elements of tho
subject.
7. Tho inela.stie tluids with which wo are lauitieally
acquainted api)roach more or less to a Ktato of perfect lluidity,
but in all there is a tendency, greater or less, of adjacent
pa<'ticles to cohere with each other. This tendency is stronger
in such fluids as oil, varnihh and melted glass, than in such as
water and mercuiy. Hence tho former are called im^hrject
or <'."."i>v."n/w (liiids.
8. The ail* which wo breathe and gases aro compressible
fluids, and aro en<lowcd with a i)eifect elasticity, so that they
can change their shape and volume by compres>ion, and when
he compressi(m ceases they can return to their former shapo
jid volume.
9. Vapours, as steam, are elastic lluids, but with this
pc(,'uliarity: at a given tempcratiu'o in a given spice only a
certain quantity of vapour can be contained, and if tho space
or the temi)erature bo then diminisheJ, a portion of tho
vapour becomes liquid, or even in some cases a soliil.
10. Before proceeding further with our subject wo nmst
explain tho meaning of some technical terms which wo sliull
have to employ frequently.
1
i
ON FLUID PRESSURE.
11. A I'lstoii is a short cyliiulor of wood
or motul, wliicli lits exactly tliu Citvity of
niii;tlicr cyliiiUor, uuJ works* Uj^* uml down
uUcniiitt'ly.
VI. A Viilvo is u closud lid ullixud to
tho end of a tubo or holo in a piston, opon
iiig into or out of si vessel, l>y niouiia of n
hin{^o or otliur sort of inovjublo joint, in sucli
a manner that it can be opened only in one
direction.
13. A Prism is a solid flfjiiro, tlio ends
of wliich are parallel eipial andsiinlliir pluno
fi^'nres, and tho sides which connect tho ends
ure parallelograms.
Tho figure represents a rectangular prism, in which each of
tho linos bounding tho surfaces of the i)ri8m is at right angles
to each of the four lines which it meets.
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14. Wo shall often have to use tho expression Ilorizontai
Section of a tube or hollow cylinder, and wo may explaiu tho
moaning of the exprcssifm by the following example:
Suppose a gunbarrel to bo placed in a vertical po.*iition:
suppose a wad to be part of tho way down tho l^arrcl with its
upper 8u. face exactly {)arallel to the top of tho barrel: tiicn
BUi>pose the barrel to bo cnt away so as just to leave tho
upper surface of tho wad exposed : the area of this surface of
tho wad is called tho horizontal section of the barrel.
15. Tlio mathematical theory of Hydrostatics is found e>i
Oil two laws, which weshidl now explain.
ON FLUID PRESSURE,
^ 16. Law 1. The force exerted hij ajiidd on any surface^
Xiilli which it is in contact, is perpendicular to that surface.
17. This law is merely a rei)etition of the defmition of a
fluid given in Art. 5, and wo can best explain its n'caniug and
applicutic»)i by an examplo.
li AB bo a cylinder immersed in a tlaid tlio pressures of
the fluid on the curved Hurface are all perpendicular to the
axis of the cylinder, and the pressure;, of the fluid on the flat
ends are all parallel to the axis.
Now It is a law of Statics that a fcrcc haa no tendency to
produce motion in a direction perpendicular to its own direction.
Hence the pressures on the curved surface have no tend
ency to produce motion in the (hrection of the axis, and the
pressures on the flat ends have no tendency to produce motion
•n a directioti perpendicular to ihe axis.
^ la Law il. Any pressure commjmicafed to the surface
oj ajiuid IS equally transmitted through the whole jluld in
every direction.
^. A characteristic property of fluids which distinLruishcs
them from sclid iKKli.s is this faculty wjjich they possess of
:ransmittn.ir equally !d all dirccliona the pressuies upphod to
their smluces.
h
11
ON FLUID PRESSURE,
5
It is of great irnpoil .iice to form a con*ect notion of the
priuciplo of "tho equal transinission of proMSuro," a priuciple
wliicli is applicable to all fluids, inasmuch as it depends upon
a property which is essential to all fluids and is not an acci
dental property, as weight, coloui, and others.
20. Suppose then t^c take a vessel A BCD, in tho form
of a hollow rectangular prism, uad place it on a horizontal
table.
Place a block of wood, cut to fit tho vessel, so that it rests
on tho base BO and reaches up to the level EF.
i
Then if we place a weight P on the t('p of the block an
additional pvcssuro P will be imposed on the base of the
prism.
Now suppose the block to bo removed and the vessel filled
with an incouipressiblo fluid up to the level o^ EF.
Suppose a piston exactly fitting the vessel to be inserted
and a pressure P applied by means of it to the surface of the
fluid at EF.
In this case tho pretaure P is transmitted by moiuis of the
fluid n()t oidy to the base BO, but also to the sides of the vessel,
and if wo take a unit ot" area, as a square iiich, in the side FO,
and a unit of area in the base BO, tlio same additional pre.i
Buro will be conveyed to each.
aV FLUID PRESSURE.
•21. That jlalda tratismil pressure equally in all direc
iiu/is maybe sheicn ccpcrimevlally in IheJ'ulloiciug iiianner:
ABC is a vessel of any sliape filled with fluid.
SLiko openings of equal area at A, B, C.
Close the ojieuings by pistons, kept at rest by such a forcd
as may be required in each case. Then it will be found that if
any addilional Coixe P be applied to the piston at A, the
same force P must be api)nod to each of the pistons at B and
(7 to prevent them from being thrust out.
If the area of the base of one of the pistons, as B, be larger
than the area of the base of the piston //, it is found that the
pressure which niust be applied to B to keej) it at rest bears
the same relation to the pressure applied to A tbiit the area
of the base of B bears to the area of ihe base of A.
22. From the preceding article it is clear that if a body of
fluid, supposed to be without weight, be confined in a closed
vessel, the pressure connnunicated to the fluid by any area in
any part of the vessel will be transmitted equally to every
equal area in any other part of the vessel.
It is owing to this fact that the use of a Safety Valve can
bo depended <ju.
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OX FLUID PRESSURE.
Thus, if tho vessel A be full of steam and the pressuro of
the steam be required to be kept down to 200 lbs. on the
square inch, if a valve B, whose area is a square mch, be
placed at any part of the vessel, and be so loaded that it will
require a force of 200 lbs. to raise it, then if the steam acquire
an increase of pressure above '200 lbs. on the square inch, the
valve vaW open, and will remain open till tho pressure of the
steam is just equal to 200 lbs. on the squaie nicli.
03 Any force, hcicever small, may by the transmission
of "its pressure through a fluid, he made to support any
weight, however large.
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Snppose DE and FH to be two vertical cylinders, con
nected by a pipe EH, and suppose FH to have a homontal
section much larger than the horizontal section of DE: tor
instance, let the area of a horizontal section ot / ^ be 400
square inches, and the area of a horizontal section a Dh bo
1 square inch. a
Now if water be poured into tho cylinders, and pistons A
and n be applied to the surface at D and /; wlKitcvcr force
we apply to A will be transmitted to each portion of the base
of the i)istou D which is equal in area to the base of the
piston A. , . , A u
Hence a pressure of lib. applied to the piston A will pro
duce a pressure of 400 lbs. ol tlio base of the piston B, and
^vill therefore support a weight of 400 lbs. placed on the
^^^ This elTcct of pressure by tho medium of a fiuid is often
called Tho Hydrostatic Paradox.
ON FLUID PRESSURE,
Examples. — I.
(1) In the experiment described in Art. 23, if the horizontal
section of the small cylinder bo \\ square inches, and that of
the larger cylinder 61 sq. in., find the weight supported under
a pressure of 1 ton exerted on the piston of the small cylinder.
(2) If the horizontal section of the small cylinder be \\
square inches, and that of the large cylinder 240 sq. in., find
the weight supported by a pressui'O of 3 cwt. applied to the
piston of the small cylinder.
(3) If the pistons are circular, the diameters being l^^ inch
and 50 inches, find the weight sup'ported by a pressure of
15 lbs. applied to the smaller piston. (N.B. The areas of
circles are as the squares of tlieir diameters.)
(4) A closed vessel full of fluid, with its upper surface
horizontal, has a weak part in its upper surface not capable
of bearing a pressure of more than 4^ pounds on the square
foot. If a piston, the area of which is 2 square inches, be
fitted into an aperture in the upper surface, what pressure
applied to it will burst the vessel ?
•
(5) A filosed vessel full of fluid, with its upper surface
horizontal, has a weak part in its upi)er surface not capable of
bearing a pressure of more than 9 lbs. upon the square foot.
If a piston, the area of which is one square inch, bo fitted into
an aperture in the upper surface, what pressure applied to
it will burst the vessel ?
i
4
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(6) If the horizontal section of the small cylinder be \\
square inches, and the diameter of the large piston 20 inches,
find the lifting power of the machine under a pressure of I ton
exerted on the piston of the small tube. (N.B. The area of
22
a circle is — times the squire of the radius nearly.)
I
ON FLUID PRESSURE.
24. The pressure at any point in any direction in a fluid
is a conventional expression used to denote tlie presauro on a
unit of area imagined as containing the point, and ijcrpendicu
lar to the direction in question.
Per examphj, if the whole pressure of a fluid on the
bottom of a vessel is 2000 lbs., and the pressure is uniform
throughout, then if we take a square in(;h as the unit of area,
and the area of the bottom of the vessel is 40 square inches.
the pressure at a point in the base is  lbs. or 50 lbs.
25. The student must carefully observe the distinction
between the expressions "pressure on a point" and "pressure at
a point" : the former is zero, because a point has no magnitude.
26. If a mass of fluid is at rest, any portion of it may bo
supposed to become rigid without affecting the conditions of
equilibrium.
Thus if we consider any portion A of the fluid in a closed
vessel, we may suppose the fluid in A to become solid, while
the rest of the fluid remains in a fluid state, or w^e may suppose
the fluid round A to become solid, while the fluid in A
remains in a fluid state.
I
I
27. The importance of the principle laid do^vn in the pre
ceding article may be seen from the following considerations.
The laws of Statics are proved only in the case of forces acting
on rigid bodies. Now since the supposition of any part of a
fluid becoming solid docs not affect t^e action of the forces
acting upon it, and since we can in thac jase obtain the effect
of tlioso forces by the laws of Statics, we shall know their
effect on the fluid.
[O
ox FLUID PRESSURE.
28. If a body of fluid, supposed to bo witliout weight, b«
confinod in a closed vessel, so a.s to cxuctly till the vessel, an
equal [Jiessure «''ill be exeited on the fluid by every ecpial
area in the sides of the vessel (Art. 22), and wo proceed to
shew tiiat the pressure is the same in all directions at every
point of the fluid.
For let be any point in the iluid, and AB, CD two plane
surfaces, each representing a unit of area, passing through O
and parallel to two sides of the vessel EF, GH. Then drawing
straight linos at right angles to AB, CD from the extremities
of AB, CD to tho sides of the vessel, we may imagine all the
tluid except that contained in tho prism ABNM to become
solid.
Then tho pressure exerted on tho fluid by the area MN
will be transmitted tf) AB.
Again, if we suppose all tho fluid except that contained in
the prism CDSR to become solid, the pressure exerted on the
fluid by tho area RS will be transmitted to CD.
Now the pressures exerted on tho fluid by the areas MN,
RS are equal, and consequently tho pressures on AB, CD
mil be equal, that is, the pressure at the point O is the same
in all directions.
Also since the distance of the point fi am the sides of the
vessel is not involved in tho preceding considerations, it
follows that the pressure is tho same at every point
^
CHATTKR H.
On the Press7ire of a Fluid acted on by Gravity.
29. In tlie preceding chiix>ter we considered tlie conse
quences thiit result from the peculiar property, essential to all
fluids, of transmitting equally in all directions the pressures
applied to their surfaces.
We have now to considor the effects produced by the
action of gramty upon the suhstavrf of a fluid.
30. The stiulent must mark carefully the distinction be
tween force ap[»lied to a surface and force applied to each
of the particles composing a body. As an example of these
distinct forces consider the case of a book resting on a table.
F(U'ce is applied to the surface of the book by the table, and
thus is counterbai<Luced the force of gravity which acts upon
each particle of uiiich the l»()ok is composed.
31. All fluids are subject to the action of gravity in tlio
name way as solid bodies. Viach ]>arti(:le of a fluid has si tendency
to fall to the smface of the earth, and in a mass of fluid at rest
there is a particular point, called the centre of gravity, at
which the resultant of all the forces exercised by the attrac
tion of the Earth on the particles composing the fluid may be
supi)osed to act,
32. The term density is applied to fluids, as it is to solid
bodies, to denote the degree of closeness with which the paiti
c'es are packed.
!i
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OM TTTK PRESSURE OF A FLUID
Wlien wc speak of a fluid of /c,«(/(jrm density, \v(3mcan that
if from any part of tlie l)ody of lluid a portion be t;ikon, and if
from any other part of tlio body of fluid n jjortion like in form
and equal in vohnno to the tovnier portion bo taken, the
weights of the two portions will bo e(inaL
33, If a vessel bo filled with a hoa^7 fluid of uniform density
the pressure at every point in tlie interior of the fluid will not bo
the same, because the pressure which results from the action
of gravity will v.ary in magnitude according to the position of
the point m the contai'ihig ve'^scl.
Consider a closed surface of small dimensions containing
the point A , and snpjioso the fluid outside the closed surface
to become solid. The fluid icithin the closed surface will
exercise pressure against the surface at evciy point, and these
liressures will 1)0 unequal, because the fluid is acted on by
gravity. But we may conceive that, if the (piantity of fluid
within the surface be cern umall^ the diflerence between the
pressuies at diflercnt points of the suiface will be very small,
and when the surface is indefinitely diminished the pressures
exercised by the fluid at each point of the surface may be
regarded as equal, and the weiglit of the fluid may be neglected.
Thus wo can consider it as the case of a weightless fluid
and apply the conclusions of Art. "28.
Hence all the planes of equal area which can ho drawn,
passing through the point A and not extending beyond fJie
small surface, may be considered to be subject to equal
presHuros.
pa
va;
de
th(
pU
th(
«
de
th(
po
ACTED ON BY Gh'A VfTY.
n
80 wc conclude that in a heavy fluid of uniform density
(1) Tho pressure will vary from point to point.
(2) Tl»e pressure will bo tho same in all dirccLionn at any
particular point.
34. Wo have next to consider in what way the pressure
varies from point to i)oint in the interior of a (luid (tf luiiform
density when it is in equilibrium, and (irst we shall shew that
the pressure is the mnie at all points in the same horizontal
plane.
Let A and B be two points in the same horizontal plane in
tho interior of a fluid of uniform density.
■•■■*,
I
Imagine all the fluid contained in a small horizontal cylin
der, of which AB \^ the axis, to become solid.
Then tho forces actinj' on the cylinder are
t pan
allel to tho axis
(1) The fluid pressures on its curved surface) perpendicular
(2) The weight of ihe cylinder j to tiie axis.
(:>) The fluid pressure on the end A
(4) The fluid pressure on the end B\
Of these (1) and (2) have no tendency to produce motion in
the direction of tho axis (Art. 1 7).
Therefore, since there is tio hon/,»mtaJ motion,
fluid pressure on end A = fluid pressure on end B.
And since, the ends being very small, the pressure at every
point in each end may bo regarded as the same,
prcssmG at point A = pressure at point B.
\.
i
14
ON THE PHKSSURE OF A FLUID
or*. The pressure at auj/ point vithin a hmvy inelnslie
ffaid, not e^rposed to externa/ presxxro, is ]>rnp(,rtioual to
the depth of that point below the surface of the fltiiiL
A
Ji
=1^
■". ■ — ~_:^z:zr^
—
1_
■ 
m
.
^
^*^^
. , —
~
__
1
— :
V ' — "' '■■■ 
J'^
■ — '^:r:s:^—
I
Let P and Q be two points at difFercnt rloptha below the
surface of tlio fluid.
Suppose two small equal and liorizontal circles to bo
described round P and Q as centres.
Then suppose the fluid in the two small vertical cylinders
PA, QB, extending from tlio bases P and Q to the surface, to
become solid.
Now tlie forces acting on the cylinder PA are
(1) The fluid pressures o\\ its curved surface, all of which
are perpendicular to the axis.
(2) The wciglit of the cylinder )
(3) The fluid pressure on the base p\ P^''''"'^ *^ ^^'' '''^^^
Of these (1) lias no tendency to produce motion in the
direction of the axis (Art. 17).
Hence since there is no vertical motion,
fluid pressure on base /* = weight of cylinder PA.
So also, fluid pressure on base Q = weight of cylinder QB.
Ilenco
pressure at point P : pressure at point Q
:: pressure on base P. pressure on base Q, (Art. 24.)
:: weight of cylinder PA : weight of cylinder QB,
:: length of PA : length of Qi?(lhe bases being equal),
::depthofP :depLh of (^.
Cor. If pressure at P = i)ressure at Q
depth of P^ depth of ^.
ACTED ON BY GRAVITY.
n
. Tho pressure of the iitinospheio on the 8urf;ico of tho fluid
is not taken into account, but we Hhall shew liLreafter how it
aUocts the pressure at a point in tho interior of a fluid.
3(5. TIm surface o/ a heaoy inelaslic jluUl at rest U
horizontal..
i^)oz:i::F=
Let A and B bo two points in tho same horizontal plan
in tlie interior t»f a heavy fluid at rest.
Suppose the iiuid contained in a small horizontal cylinder
uf fluid, of which ABh the axis, to become solid.
Then, fluid i)ressuro on cud A = fluid pressure on end B
(Art. 34), and, since the ends are equal,
fluid pressure at point A = fluid pressure at point B
Hence A and /; are at tho same <lepth below the surface
of tho fluid (Cor. Art. 35), and if we draw AC, Z?Z> vertically
to meet the surface in (7, Z>,
AC=BD,
also, ^C is parallel to BD ;
.. CD is parallel io AB (End. i. 33) •
. . CD is horizontal.
Similarly any other point in the surface may be proved to
be in the same liorizontal plane with C or Z> ;
.•. tho surface is horizontal.
37. The proposition thai the surface of a fluid at rest
is horizontal is only true when a very moderate extent of
surface is t\ken.
Larj^e surfaces of water assume, in consequence ol the
ati>i'au
tion exercised bv the earth, a spherical form=
i6
ON THE PRESSURE OF A fLUID
The following practical msults aro worthy of notice :
(1) All lluids (iiid thoir lovol. If tiiboH of vurioua shapes,
Boiuo largo uiul sonio Hinall, soino Htraii,'ht uu«l oiliorH bent, bo
placed in a closed vessel full of wjiter, iind water be tlieii
poured into one of the tubes, the lluid will rwe to a uniform
height in it and all the other tubes.
(2) It pipea bo laid down Ironi a reservoir to any
distance, the tluid will mount to the same height as that to
which it is raised in the reservoir. •
(3) The suiface jf a lluid at rest furnishes a means kA
observing objects at a distance in the same horizontal plane
with a mark at the place of observation.
38. Wo have seen that in an inelastic lluid at rest the
pressure at any point depends on the depth of that point
below the surface of the lluid, that is, on tle lengUi ot the
vertical lino ilrawn from the [)uint to meet ii horiznntal lim
drawn througli the highest point in the fluid.
Thus if ABO be a conical vessel with a horizontal base,
standing on a table, and lilled with fluid, the jjressure at any
point P is determined in the following manner.
r. 1
ii
From yl, the highest point of the fluid, draw a vertical lii] j
meeting the horizontal plane passing through P in the point <;>
Then the pressure at /» = pressure at Q, because P and Q,
are in the same horizontal plane.
But pressure of Q depends on the length of AQ;
therefore pres.vr re "> P fleponds on the length of PR, a line
drawn verticallv to i;;eei the horizontal line AR,
ACTED ON BY GRAVITY.
»7
39 If a te%9eU '\f ^hlch the hotfom u horizontal and
{hemh's rerticd, he jUhd with Jlnid, thn pres>sure on Uu
boUom will be equal to the weight q/'thejluid.
Vlg. I.
Fig. II.
Fig. ni.
Let ACDB (fig. I.) bo a vessel whoso bottom, CD, is hori
zontal, and its sides vertical. Wo may consider tho fluid in
this vessel to bo niado up of vertical columns of fluid. Each ol
tiiese columns will press vertically downwards with its weight,
and the sum of these pressures will bo tho weight of tho fluid.
Now tho base of the vessel, being horizontal, will sustain all
those vertical pressures ;
/. pressure on tho base of tho vessel = weight of the fluid.
If tho sides of tho vessel be not vortical, as in figs. II. and
III tho pressure on tho base will bo equal to tho weight of a
column of fluid ECDF, EC and FD being perpendicular to
CD, and EF being tho surface of tho fluid.
Ileiico if in tho throe vessels tho bases aro equal and
on the same horizontal plane, and tho fluid stands at tho same
height in tho vessels, the pressure on tho base in each case
will be tho same.
The fluid in vessel I. produces a pressure on the base equal
to its own weight.
The fluid in vessel II. produces a pressure on the base less
than its own weight.
The fluid in vessel III. produces a pressure on the base
greater than its own weight.
i8
ON THE PRESSURE OF A FLUID
EXA2 PLES.— IL
(1) If the pressure at a depth of 32 feet 1)0 lo lbs. to the
square inch, whi>t will the pressure be at a depth of 42 feet
6 inches ?
(2) If the pressure at a depth of 8 feet be 14^ li'>s. to the
square '.ucli, wiiat Avill bo the pressure at a depth of 20 ft. 6 in./
(3) III tv'o uniform fluirls the pressures are the same at
the depths of 3 ahd 4 inches respectively : compare the
pressures at the depths of 7 and 8 int les respectively.
(4) In two uniform fluids the pressures are the tame at the
depths of 2 and 3 inches respectively : compare tlie pressures
at the depths of 9 and 12 inches respectively.
(5)* Find the height of a column standing in water 30 feet
deep, wheu the pressure at the bottom is to the pressure at
the top as 3 to 2.
(6) If the pressure of a uniform fluid, not exposed to
external pressur',', bo 1 .5 lbs. to the square inch at a depth of
15 feet, what will be the pressure at a depth of 12 feet ?
(7) If the pressure of a uniform fluid, not exposed to
external pressure, bo 3 lbs. to the square inch at a depth of
4 feet, w!iat will be the pressure on a uquure inch at a depth of
12 feet?
(8) What is the pressure on tlie horizontal bottom of a
vessel filled with w^ater to the depth of 2^ feet, the area of the
base being 20 square feet, antl the weight of a cubic foot of
water 1000 oz. '\
(9) A cubic foot of mercury weighs 13G00 oz. Find the
pressure on the horizontal base of a vessel containing mercur},
the area of the base being 8 square inches, and the depth of the
mercury 3 inches.
(10) What is the pressure on the horizontal base of a vessel
filled with water to the depth of 15 feet, the area of the base
being 24 square feet, and the weight of a cubic foot of water
iOOO oz. ]
(11) A cistern shaped like an equilateral triangle of which
one side is fi feet is filled with water to the depth of two feet :
find the pressure on the base, the weight of a cubic foot of
water beiiii? 1000 oz.
. f
hi
ACTED ON BY GRAVITY.
19
i
J
(12) The spout of a teapot springs from the middle point
of one side, and its upper extremity is on a level with the lid.
If tlie spout be broken oiY halfway, how high can the teapot bo
filled ?
(13) When bottles that have been sunk in deep .vater have
been brought up, their corks have been found driven in. How
do you explain this \
(U) If a pipe, wjose height above the bottom of a vessel is
112 feet, be inserted vertically in the vessel, and the whole be
filled with water, find tlie pressure in tons on the bottom of
the vessel, the :irea of the bottom being 4 square feet, and tlie
weight of a cubic foot of water 1000 oz.
(15) A hole, a square inch in area, is bored in the flat
cover of a vessel full of wacer, and a smooth piston weighing
7 lbs. 13 oz. is fitted into it ; a vertical tube is then fitted into
another hole in the cover, and water is poured iuto it: find
how hi«h the water must be made to ascend in it in order that
the piston may be driven out, a cubic foot of water weighinij
»,;
«2
^
; ?*ii
I I
m
*c
CHAPTER III.
Oh Specific Gravity.
40. Some substances are from the nature of their conn)o
sitioii more weighty than others. We call gold a heavier metal
than lead, because we know by experience that a given volume
of gold is more w eighty than an equal volume of lead.
41. Wo make a distinction between the terms weight and
weightiness.
We si;eak of the weight of a particular lump of gold or iron.
We speak of the weightiness of gold or iron, not referring
to any particular lump, but to the special characteristics of the
metals in question.
Further we say that gold is heavier than iron, having no
particular lumv) of tlio metals in viovv, bnt expressing our
notions of the degree of weightiness tliat is peculiar to either
substance.
This degree of weightiness is known by the name Specific
Gravity.
Def. The Specific Gi'avity of a suhstancc is the degree of
weightiness of that substance.
42. If of two substances, one of which is twice as weighty
as the other, we tidce two lumps of equal volume, the weight
of one lump is evidently twice that of tlie other : and, generally,
if one substance be /S' times as weighty as the other, the we'ght
of any volume of the first is ,S' times the weight of an equal
volume of the other. Now l>y a sulistuice, the measure of the
specific ! ravity of which is aV, wo mean a substance which is S
times as weighty as the standard by which specific gravities are
estin)ated. Tiierefore any volume of this substance will weigh
S times as much as the equal volume of the standaid.
i
ON SPEC I FTC OR A VITY.
21
i
43. Tho requisites for a Standard are that it should be
definite and uniform, and these requisites are possessed by
Pure Distilled Water at a certain temperature. This substance
is therefore taken as the standard for estimating the specific
gravities of solid bodies and inelastic fluids.
44. When we say that the specific gravity of gold is 19,
we mean that tho specific gravity of gold is 19 times that of
Pure Distilled Water, and therefore a given volume of gold
weighs 19 times as much as the same volume of distilled water.
45. To measure the Weight of a body we must have a unit
of weight, and to measure the Volume of a body we must have
a unit' of volume. These units we may select in any way that
may suit our purpose, and we connect them with the unit of
specific gravity by the following convention :
The unit of specific gracity is the specific gravity of that
substance of which a unit of volume contains a unit of iccight.
46. To find the numerical relation existing between the
measure of the specific gravAty of a substance and the mea
sures of the weight and volume of any given quantity of the
substance.
Let W represent the measure of the weight of a substance,
that is the number of times it contains the unit of weight.
Also, let V represent the measure of the volume of the
substance, that is the number of times it contains the unit of
volume.
And let S represent the measure of the specific gravity of
the substance, that is tho number of times it contains the unit
of specific gravity.
Then one unit of volume of this substance will weigh S
times as much as a unit of volume of the standard substance,
^Art. 42) that is, its weight is 6' times the unit of weight.
Therefore the weight of V units of volume is VS times
the unit of weight ;
therefore the mcusure of the weight of V units of volume
of the substance is VS ;
but tliis measure we have denoted by W\
• \V^ VS.
r)
i
i;^!l
.1
■ St!
f
22
ON SPECIFIC GRA VITY.
47. The equation W^ VS gives us merely the relation
between three nunil)cr.s, and two of these must be given ii)
order that .ve may determine the third.
When we have found it we know the mm^/oe of the weight
or volume or specilic gravity, as the ease may be, and we must
have the unit of weight, (,i of volume, or of s]),xific gravity aI«o
given to enable us to determine the weiht or volume or
specifie gravity of a partieular substance. So that we may mi
it thus :
i
measure of weights VS,
measure of volume 
W
»1. »,
•md
JV
measure of specific gravity = — ;
weight = Fas' times (unit of weight),
W
volume = ^ times (unit of volume);
TT7
.specific gravity = p times (unit of specific gravity).
■ ■
48. A cubic foot of pure distilled water at a temperature
of 62« Fahrenheit weighs about 998 oz., and for rough calcula
tions it is assumed that the weight of a cubic foot of water is
lOOO ounces.
Then if we take 1 cubic foot as our unit of volume and pure
distilled water as our standard of specific gravity the unit of
weight will be 1000 ounces.
Or if we prefer to take 1 lb. avoirdupois as our unit of
weight and pure distilled water as our standard of specific
gravity, the unit of volume will be j^^ of a cubic foot, that ia
OiG cub. ft.
aV SPECIFTC GRA VITY.
23
H 1
49. We shiill next explain how quantities are mensiired ;
and then we sliall give three examples, worked out first on tho
supposition that 1 cubic foot is taken as the unit of volume, and
secondly, on the supposition that 1 lb. avoirdupois is taken as
the unit of weight, so that tho student may see that the same
result must follow from both suppositions, and that such a
choice may bo made as to the units as may be suitable to any
particular case.
50. To measure any quantity we fix upon some definite quan
titv of the same khid for our standard, or unit, and then any
quantity of that kind is measured by finding how many times it
contains this unit, and this number of times is called tho
measure of the quantity.
For example, if one pound avoirdupois be the unit of weighty
the measure of 16 lbs is 16. Or, to put our calculations in a
tabular form, we may give the following Examples :
"X.,
h
s
Unit.
1 lb. avoird.
1 lb. avoird.
1 lb. avoird.
1 cub. ft.
1 cub. ft.
1000 oz. av.
•016 cub. ft.
Quantity.
8 lbs.
4 oz.
1 lb. troy.
6^ cub. ft.
3 cub. in.
14 lbs. av.
b cub. in.
Measure.
8.
1
4*
5760
7000 *
65.
.3
1728 '
14x IG
1000 •
r728~)r Ole '
l€
■ I '■
24
ON SPECIFIC GRA VIT Y.
61. First, when 1 cubic foot is taken as the unit of volume,
and consequently 1000 oz. as the unit of wciglit, to solve the
following examples :
Ex. (1) The specific gravity of load is ir4, find tho
weight of 720 ciihic inches of lead.
Hero r=/i«, 5=114.
Weight required = VS (unit of weight)
720 \
~ ( r2s ^ ^ ^ "^ ' ^^"^^^^ ^ ^"" ^^'
= 4750 oz.
Ml
\
= 296 'lbs.
o
Ex. (2) If 5 cubic feet of a substance weigh 240 lbs., what
is its specific gravity \
TT rjfr 240X16 ,^ ^
Here W= — — ^ , r= 5.
iOOO
w
Sp. gr. required = v^ (unit of specific gravity)
240 X 16
—    (unit of specific gravity)
240x16
(unit of specific gravity)
lUU0x5
= "768 (unit of specific gravity).
Ex. (3) What is the volume of a substance whose specific
gravity is 9*6 and whose weight is 4200 lbs. ?
.. TT^ 4200x16 ^ ^
• Here^=j^^,^ ,.9=9'6.
Volume required == v (unit of volume)
4200 X 16
1 000
: 7 cub. ft.
culx ft.
^\
i
■^iE«ias*»«»«»»««»'«»«*«»' .i^^g^^^ ^. .«■... r
ON SPECIFIC GRA VITY.
25
52. Secondly, when 1 lb. avoirdupois is taken as the unit
of weight, and consequently '016 cub. ft. as the unit of volume,
our examples will stand thus :
ti
ft
Ex. (1)
Here
r=
720
172s X 016
, aS'=114.
^V^ eight required = VS (unit of weight)
~ X ^ X \\'^ times lib.
28 016 /
= 296 lbs,
(5
'i
Ex. (2)
Here
rF=240, V
W
•01(j
Sp. gr. required = 77 (unit of specific gravity)
i,^h
I
240
5
•016
(unit of specific gravity)
240 X 016
(unit of .specific gravii;
1 08 (unit of specific gravity).
I
Ex. (3)
Hero W^=4200, *S'=96.
W
Volume required = ;t (unit of volume)
4200 ,.
=; tmies
WKy
•016 cub.
i^
4200
9() X
xl6
1 000
cub. ft.
^ 7 cub
.ft.
m
if
f I
i J1
J
1
■1
^
«6 gy SPECIFIC GKA V/TY. ^
f).']. If a iinniber of substances be put tojjctlier to form a
mixture, wo shall gmerally have the following relations :
(1) sum of measures of weights of compounds = measure of
weight of mixture.
(2) sum of measures of volumes of compounds = measure of
volume of mixture.
Thus if «<7i, w^, w^ bo the measures of the weights,
ri, tv «?3, volumes,
Sj, S2, s..j, specific gra
\aties of the compounds, and
w, V, s the measures o^ the weight, volume and
specific gravity of the mixture, we shall have
Wi + Wj + '^'3 + '^t
i\^i\^ + v.^+ =»;
and therefore
U'l ^2 w^ _w
_ . I_ — f. f".. — ""•
h .'fl h «
Note. We say that these relations hold generalbf, because
in some cases, when substances nre mixed, tlie volume of the
mixture is not equal to the sum of the volumes of the two
substances. For instance, 70 pints of sulphuric acid mixed
with 30 pints of water will make a mixture of less thaii ODphits.
54. In applying these formula; to the solution of examples,
we may take any unit of volume or of weight, adhering to
it through the whole cidculation.
Ex. (1) To find the specific gravity <;f a mixed metal com
posed of 5 cubic inches of copper, specific gravity 9, and 8 cubic
iaclies of tin, specific gravity 7'2.
Since i\ s^ + v^ s^ — ??.<?,
if wo take 1 cubic inch as the unit of volume, we ha e
5x9 + 8x72 = (5 + 8).9;
..*= — ,.,  / "90 nearly
13 "'
i
ON SPECIFIC GRA VITY.
27
Ex. (2) Ten pfninds of fluid, specific jjravity I'Or), are
mixed with 15 pouiuls of distilled water. Find the specific
giavity of the niixturo.
Since
Wj w„ w
' + —' = ,
1 2 *
if we take 1 lb. as the unit of weight, wo Ikivo
10
15 25
105
1
5_5;15
•*'.9"l05'
105x5 105 ,^,,^ ,
/. 8^ — — =  =roi9 nearly.
615 lu:{ •'
1^1
55. The Density of a substance is the degree of closeness
cith which th^ 'particles composing the substance are packed
"ogether.
The difference between density and specific gravity may
be stated thus : in estimating the density of a body we take
into account the quantity of matter contained in a given
volume : in estimating the specific gravity of a body we take
into account the effect of the action of gravity on a given
volume.
If we cake t!ie same substance, as pure distilled water,
as that to wdiich we refer as a standard in measuring the
doi ^r>\ specific gravity of another substance, the
mea? : the density and specific gravity will be the
same.
Examples. — III.
'M (1) The specific gravity of copper is 8"91 ; find the weight
of 512 cubic inches of copper, a cubic foot of water weigliing
1000 oz,
(2) If 4 cubic inches of iron weigh as much as 72 cubic
inches of amber, compare the specific gravities of iron and
amber.
'I
8
ON SPECIFIC OR A VITY.
(3) Tho specific gravity of mercury being 13'3, find tho
weight of one cubic inch of it, liiiving given that a cubic foot of
water weighs 1000 oz.
(4) If two cubic feet of a substance weigh 100 lbs., what is
its specific gravity ?
(5) Find tho weight of 36 cubic inches of cork, whoso
specific gravity is 024.
(6) A cubic foot of water weighs 1000 oz., what will bo
the weight of a cubic inch of a substance whoso specific j^riivity
is 3?
(7) What is the specific gravity of a body of which m
cubic feet weigh n lbs. 1
(8) Five cubic inches of iron weigh 22i oz., what is tho
specific gravity of iron?
(9) Twelve cubic feet of dried oak weigh 875 lbs., what is
the specific gravity of the wood ]
(10) Twentysix cubic feet of ash weigh 137Hlbs., what is
its specific gravity ?
(11) A metal, whose specific gravity is 15, is mixed with
half the volume of an alloy whose specific gravity is 12, find the
specific gravity of the compound.
(12) Two metals are combined into a lump the volume
of which is 2 cubic inches ; ^ h cubic inches of one metal weigh
as much as the lump, and 2J;r cubic inches of the other metal
weigh the same. What volume of each of the two metals is
there in the lump ?
(13) • Two substances whose specific gravities are 1"5 and
30 are mixed together, and form a compound whose specific
gravity is 25 ; compare the volumes and also the weights oi
the two substances.
(14) The specific gravity of seawater being r027, wlmt
proportion of fresh water must be added to a quantity of
seawater that the specific oravity of the compound may be
10091
I
ON SPECIFIC GRAVITY.
29
and
(15), Eqtial woijflits of two siibMtancos whoso densiUoH are
3'2r) and 2"75 arc mixed tojjcther ; find tlio density of the
compound.
(16) Equal vohnncs of two substances whoso specific
gravities aro 25 and r5 are mixed to^jetiior; wliat is the
specific gravity of the compound ]
(17) Five cubic inclics of load, specific gravity irn5, aro
mixed v.ith the same volume of tin, s[)ucific gravity 73; what is
tlie specific gravity of the compound /
(18) A mixture is formed of e<iual volumes of three
fiuids ; the densities of two aro given and also the density
of the mixture. What is tlio density of the third fluid?
(19) Ten cubic inches of copper, sjiecific gravity 8'9, are
mixed witli seven cubic inclies of tin, specific gravity 73 ; find
tlio specific gravity of thy compound,
(20)% Three fluids, wiioso specific gravities are 7, *8 and 9
respectively, are mixed in tlio proportion of 5 lbs., 6 lbs., and
7 lbs. What is tlie specific gravity of the mixture I
(21) Tljo specific gravity of pure gold is l!)3 and of copper
8'62 ; required the specific gravity of standard gold, which is a
mixture of eleven parts of gold and one of copper.
(22) When 6J1 pints of sulphuric acid, specific gravity 1*82,
are mixed with 24 pints of water, the mixture contains only
86 pints, Wliat is its specific gravity \
(23) If three fluids the volumes of which are 4, 5, 6 and
the specific gravities 2, 3, 4 are mixed togetlier, determine
the specific gravity of the compound.
(24)* The specific gravity of quartz is 262, and that of gold
19"35 ; a nugget of quartz and gold w^ciglis 115 oz., and its
specific gravity is 7'43 ; find the weight of gold in it.
(25)*» An iron spof n is gilded, and the mean specific gravity
of the gilded spoon is 8; those of iron and gold are 7'8 and
1 9"4 : find tlio ratio of the volumes and weights of the metals
employed.
■)::i
i.
►•
'ii
t:;
CHAPTER IV.
On the Conditions of Equilibrium of Bodies under the
Action of Fluids.
5f). Wjimn a body is wholly or partially immersed in a fluid,
it is a ^eiierMl priuciijlo of Hydrostatics that the. rmdtaiit.
pressure oft/tejlidd on Ui.a snrfice of the hodij h cqntd to the
weigid of the f aid dhplaeed. This principle \vu shall prove
for two cases in Articles 57 and (jl.
(l; When the body is icholly immersed in the fluid :
(2) When the body is partially inn)ier,sed in the iluid.
57. To find the remdtant Pressure of a Fluid on a body
y'hohy mi?ncrsed and foatinff in a fuid.
^ Lot A be a body floating in a fluid and wholly immersed .
m it.
!
the
L fluid,
ultaiif,
to the
prove
lid.
\ body
M
ON THE COrrPITIONS OF EQUHJnRIUM ^c, 3 1
Iiiuij^Mno tlio body roniovcd and tlio vae;mt Hpaco (illod uitlj
fluid of tlio saiu(; idui as tliat in which tho hody floated.
Tlien suppose this substituted fluid to become solid.
Tho pressure at each point of its surfiico will still bo the
Banio as it was at the same point of the surface of .4
Tho solidifled fluid is kept at rest by
(1) Tho attvactio"! exercised by tho earth on every par
ticle of its mass :
(2) Tho pressures exorcised by the fluid at tlio diflereut
points of its surface.
Ilonco the resultants of these two sets of forces must be
eqmd in ma<jnitadc and ojjptjsilc in their lines of action.
Now tho resultant of set (I) is called the weight of the
solidified fluid and ;icts \cxW<^\Ac!j downwards througii its centre
of gravity.
Hence the resultant of set (2) is equal in magnitude to tho
weight of tlie solidified fluid and acts veitically upicards
through its centre of gravity.
Now since the proL^sures on the solidified fluid are tho same
as on tho body A, we see that the resultant pressure of tho
fluid on A is eipial to the weight of the fluiil disj)laced by A
and acts vertically upwards tlirough the centre of gravity of
this ,disj)laced fluid
This principle we shall now apply to tho following Ex
amples in ytatics.
li
5rsed
58. Ex. I. Find tlie conditions of cqidUhrium of a body
floating in afiiid and tcholly immersed in it.
Tho body A (see diagram in Art. 57) is kept at rest by
(1) Its weight, acting vertically downwards through its
centr'> of gravity :
(2; The pressures of the fluid on its surtacc, the resultant
of which is equal to the weight of the fluid displaced by A and
iicts vertically upwards through the centre of gravity of the
fluid displaced.
I
.11
► • I'
hi
32
,___S^^{^^^jCC^D£TJONS OF EQUILIBRIUM
Hence
(1) Weiglit of A  weight of fluid displaced by A :
(2) The centres of gravity of ^ and of the fluid displaced
are in the same vortical lino.
These are the conditions of equilibrium.
Note. A difiiculty often occurs with beginners in conceiving
how a solid body can be in equilibrium in the midst of a
fluid, neither rismg to the surluce nor sinking to the bottom
It may however be proved by experiment that a hollow ball
of copper, such as is used for a balltap, may be constructed
(>f such a weight relatively to its size that when placed in water
It will remain where it is placed, just as tlie body A is re
presented in the diagram,
59. Ex. II. Find the conditions of equilibrium for a
body of uniform density wholly immersed in a fluid and in
part supported hy a string.
Let a body the measure of whose volume is V be suspended
.^a st„,.g fron, t„. fixed point A .0 a, to flo.t bc.owrt'
The body is kept at rest by
(1) its weight,
(2) the pressures of the fluid on its suritxce,
\v>j tlie tension of the sti'ing.
fi
i
w
BODIES UNDER THE ACTIO N OF FLUIDS. 33
ItDW (1) is equivalent to a single resultant acting vertically
doicnwards through the centre of gravity of tho
body ,
(2) is equivalent (by Art. 57) to a sinj^lo resultant,
equal to the weight of fluid displaced and acting
vertically upwards through tho centre of gravity
of the fluid displaced :
(and these two centres of gravity coinciding)
therefore (3) must act (see Statics, Art. 52) upicards in the ver
tical lino through this common centre of gravity^
and (1) must be equal to the sum of (2) and (3).
Hence, if
*S' be the nie;isure of the specific gravity of the body,
^' ofthe fluid,
^ of the tension of the string,
there is equilibrium when
or r= v(ssr),
Ex. A piece of metal, whose specific gravity is 73 ano
volume 24 cubic inches, is suspended by a string so as to be
wholly immersed in water. Find the tension of the string.
Taking 1 cubic inch as tho unit of volume, and conscqueJi*^*
„ oz. as the unit of weight,
■I
■\:
m
1000
tension of string = 24 (73  1) x ^ oz.
1 /28
24x6;^ X 101 »0
1728
OS,
^8Y5oz.
0.B.
8
34 ON THE CONDITIONS OF EQUILIBRIUM OF
60. Ex. (3) // a body of unif^'^\ i dcnsit>j be immerned
in a fluid and he prevented from rising hy a string attached
to the bottom of the vessel containhuj the fluids find the
tension of the string.
\
\i
— ../
rl
'i is
'■ ti
It
Hi
Let a body, tlie measure of whose volume is V, be kept
under the surface of a fluid by a string fastened to J, a point
in the base of the vessel.
The body is kept at rest by
(1) its \teight, acting vertically downwards,
(2) the tension of tiie string, acting vercieally down
wards,
(3) the resultant of fluid pressures on the body, acti'f^?
vertically upwards.
Hence, if
T be the measure of the tension of the strinf>,
^ specific gravity of the body.
^' specific gravity of the fliiidj
since there is equilibrium,
.'. 7'= ys' vs
BODIES UNDER THE ACTION OF FLUIDS. 35
Gl. To find the resultant presti.ire of a fluid on ii lody
partially immersed andfioaling In the fluid.
\m
Ill
Let ABCD be a body partially immersed and flnatmg iu
a fluid, the part BCD being below the surface of thvi tiaid.
Imagine the body removed and the vacant space BCD
filled with fluid of the same kind as that in wiiich the body
floated.
Then suppose this substituted fluid to become solid.
The pressure at each point of its surface will still be the
same as it was at the same point of BCD.
The solidified fluid is kept at rest by
(1) the attractions exercised by the Earth on every
particle of its mass,
(2) the pressures exercised by the fluid at the different
points of its surface*
Hence the resultants of these two sets of forces must be
equal in ma(jnitude and apjyosite in their lines o/actio?i.
vacuum.™"'''''""* *'"^ t'i''Ptcr tlie space occupiod by the air is supposed to bu a
3—2
i
rij
centre of gravity '"'""^ downward, through its
through its centr?of glvit!:^ • "" "'^ ™'^'^''"^ "^'^
as o'LThf;;n::sTe::elhaTt,fir Tr "~
m S""""'" "' '"■'" ""' "»'P'^ "> '"e following example.
I'
I'
•■i
J
62. Ex. I. FindthecondUionsofeoidUhrium nf^h ^
floaung and partially immersed iTZrcflr''^''
density. ^^^^ ^f uniform
The body ABGD (see diagram in Art. 03) i. kept at rest by
o/gr!^ity!'°''' '"™^ ""'"""'^ downwards through
centre
its
Hence
(1) weight of the body = weight of fluid displaced ;
uispiaiir!:irr/.a,i"'^ •^"^ ""^ ' "'^ ^'^
Tliese are the conditions of equilibrium.
i
I
BODIES UNDER THE ACTION OF FL UIDS. 3 7
63. Ex. II. When a hody of uniforin demify floats in
a fluid, the volume of the part immersed is to the volume of the
whole body a the specific gravity of the hody is to the specific
!j racily of thejc uid.
f
Let Fhc the measure of the volume of the whole body ABCB
V' '
• part immersed BCD,
^ specific gravity of the body,
^' specific gravity of the fluid.
Then since, Art. 62,
weight of floating body = weight of displaced fluid,
'\V' : V :: S '. S\
Ex. A solid, whose specific gravit^y is '4, floats in a fluid
vvhosc specific gravity is 12. What part of the solid is below
(lie surface?
Let X bo the measure of the part immersed
m the measure of the whole body.
Then co : m=4: : 12;
'4 4 1
ii
'Mi
i
I! f
P
I.
3^__0JV_77^ CONDITIONS OF EQUILIBRIUM OF
64. The Hydi'osfatic Balance.
Jho IT^/drosfatic Balance is a conin.on balance wUli a
hook attached to the bottom of one of the scales from wh ch
a solid may be suspended and wei.^hed successively (1) in air
and (2) when immersed in a fluid.
Call the scale to which the hook is attached A and the
other scale B Then by the weight of the solid in air we mean
tJie weight which when placed in i? balances the solid suspend
ed in air from A.
And by the weight of the solid in the fluid we mean the
weight which when placed in B balances the solid suspended
trom A so as to be immersed in the fluid.
The diff'erence between these weights is caused by the
pressures of the fluid on the surface of the solid, the resultant
ot these pressures being a force acting vertically upwards and
eqitimlent to the weight of the fluid displaced hy the solid.
Now if Fbe the measure of the volume of the solid,
'^ specific gravity of the fluid,
measure of weight of fluid displaced by the solid = VS'.
Go To compare the specific gramties of a solid and a
niiid by means of the Hydrostatic Balance.
Let Fbe the measure of the volume of the solid,
\ spcLiflc gravity of tiie solid,
5; specific gravity of the fluid.
weight of the solid in air.
2
?/
a]
ai
/BODIES UNDER THE A C TIOM OF FL UIDS. ,3
Case I. When the solid is of greater specific gravitij than
ihefiidd.
Let W bo tho measure of tlio weight of the solid in the flui.l,
then W J^' = thc measure of the weight of fliiiil displaced
b> the solid,
= VS'.
Also w^ VS ; '
. VS __ IV
"'VS'~ TVJV"
or, '?; = _./Z
S' WW"
and thus S and .S" may be compared.
Case II. Whan the solid is of less specif c gravity than
the fiuid.
Attach to the solid sonic heavy substance, called the sinker,
which will make the solid sink with it in the fluid.
Let w be the measure of the weight of the two bodies in air,
^ in the fluid,
y sinker in air,
^ in the fluid
Then
«? a? = measure of weight of fluid displaced by the two bodies,
y~^= the sinker.
Subtracting,
?c;i; 2/ + ;? = measure of weight of fluid displacedby the solid
= VS';
also W=VS\
• '^^1/ + ^ __ S^
" W ~"S'
and tlms S and S' may be compared.
i
!$
«
IT?!
II . .3
40 o^ /^:f av^^ov..^^,^,,,^^,,,^ ^^
fie. The eommou IlydromeUr. "
Tlio common Hydrometer cniwists ,.f „ , • ,
terminating in t,vo hollow s„hc 1 r ^ r^"" ''^'"" ^'^
loaded witl> mercnry, so tliTtt i, V"'' ^ ^^ '» "■""""y
fluid with the stem vertL """•""'«»* may float in »
Of wl,ieh it ean be t" ," ^t :;' ', ^™r"™^ "^ '"^•™^
the surface of the fluid in wWeh [t fll": '" ™"'°"' '' ''''°"
Whose ':;"„: "t^t^" .f ^ ««"• "" "«»>•« of
bulk of thepart^immlred L r"'' "" ""^ '""''^"™ "^ «"•
whol's^ed;: gnX'is!;^^^"' '^ """'^ "'" •»™ «'
bulk of the Par'inn;,l^,H;7''"^'' "'"' "'" ""''^'■^« "' «'^
Ihen weight of hydr„„,oter = ,veight „f fi.t fluid displaced
«nd weiMit nf 1 7 ~ '"'"^^ "'® ™'* «f weight ;
«cl we.JU of ■Odrometer = ,voigl„ of second fluid disXced
 V\ S' times the unit of wei^ht •
'^^^r,^:!^^^'' »'and . are
67. Nichohon's Hj/dromeler.
3
II
I
are
An iron stirrup fl«d „ th„ 7 "f \8"PPorti„g a dish O.
dish i> A flno wen Ifi 'r«^<""' »f ^ ^Worts a hoavv
on the steel wire "'"■'''"^'"' ""k is placed at some point I
This instrument is used for two purposes :
^_^.(1) To compare the specific gravities of a solid and a
ea«st\iril;d™uerrsil''' n"1f"/'''^'' P'^^^ ™ <^'
the fluid mceL rlel .iZt T" "" "" "" ""'^"'o "^
addr^:rei,t'^;re':jf;rr^^
Then measure of weight of solid in air = TV X,
in the fluid= JV^ y
.. measure of weight of fluid displaced by solid
= {TVX)(^WY
= Y~Xi
. ».G. of solid _ IV X
8. (jr. of fluid Y—X '
t x
t
Ih *
H\
13 1 '
'§:,:
ii
lii
It:
ii
1
If'*
Is 1
43 aV T///^ COMDTTIONS OF EQUriJIUUUAf OF
(2) To compare tlic spociHc gravities of two fluif]'^.
Let IVXiii the mcaynre of tlio weight of the hytlrometcr,
X ami y the mcisurcs of weight to bo placed in C to make the
inslrninent sink to B in each iluid.
The inoasuro of weigl»t of first fluid displaced  \V+x,
sec(/nd = ^^+1/,
and, since the volume is the same in both cases,
S. 0. of first fluid JV+x
S. (r, of second fluid ~ W+y'
68. To compare the specific gramtics of two JJinda by
ii'ciffJi lug the same solid in each.
Let S and >S" bo the measures of specifie gravities of the
fluids,
tv> and ?// the measures of weights of the solid when
immersed in the respective fluids,
W tlic measure of weight of the solid in af".
Then IFwjmeaturo of weight of fluid displaced by
solid in one case,
)!r?y'= measure of weight of fluid displaced by solid
[u the other case ;
and thus S and S' may be compared.
Examples. — IV.
(1) A piece of glass when weighed in water loses ^i^ijths
of its weight; what is its specific gravity?
(2) Find the pressure on 28 miles of a submarine tele
graphic cable whose c'cumference is .3 inches, the depth of the
cable below the surface of tiio sea being 480 feet, and the
specific gravity of sea water r026.
(3) A body whose specific gravity is 3*3 floats on a fluid
whose specific gravity is 44 ; what portion of the body will be
immersed %
(4) If the specific gravity of standard gold be 19"4, and the
weight of a .sovereign in air bo 5 dv/ts. 2 grs<, find its weight
in water.
/
BODIES UNDER THE ACTION OF FLUIDS. 43
(5) If a Bubstancc weigh 8 lbs. iu air aiid 6 lbs. in water,
what is its specific gravity ]
(G) A cylindrical tub of given weight floats witli one fourth
of its axis below the surface of a fluid : find the least weight
which will totally imnierso the tub.
(7) A body whoso specific giavity is 1*4 floats in a fluid
whose specific gravity is 21; what portion of t'no body is im
mersed ]
(8) A leaden bullet, weighing 1 oz., is placed in a glass
of water standing on a table ; find the pressure of the bullet
on the bottom of the glrss, the specific gravity of lead being
ir4.
C^) A cubic inch of cork floats in water ; find the weight
which must be placed upon it to cause the half of it to be im
mersed, the spec; fie gravity oF cork being '24, and the weight
of a cubic foot of water 1000 oz.
(10) A cork, whose ^\eight is \ oz. and specific gravity '25,
is attached by a string to the bottom of a vessel containing
water so that the cork is wholly immersed. What is the ten
sion of the string 1
(1 1) A person supports a ball of load, weighing 46 oz. and
of specific gravity ITS, wholly immersed in water, by holding
the end of a string attached to the ball. What is the tension
of the string 1
(12> A vessel containing water is placed in one scale of a
balance and weighs 1 lb. A piece of wood of specific gravity
•24 and volume 1 inch is attached to the bottom so as to be
immersed. What weight will now balance the vessel ?
(13) A cube har ging by a string is half immersed in water.
If the weight of the cube be a pound, and its specific gravity
three tmies that of water, what will be the tension of the string ?
(14) A certain substance weighs 30 oz. in water, and 42 oz.
out of water. What is its specific gravity ?
(15) A substance weighs 14 lbs. in water and 2560 oz. out
of water. What is its specific gravity 1
!:f!
ti
%m
44 ON THE CONDITIONS OF EQUILIBRIUM OF
i !i
[»
ij
I !
(16) A substanco wcigliH 12oz. in air : a substauco weigh
ing 20 oz. in water is attacliocl to it, and tlio two together weigh
• 18 oz. in water. What is tlio 8i»eciUc gravity of the I'ormer
substance ?
(17) A picco of mahogany weiglis in air 376 grains, a
piece of brass weighing 3so grains in water is attaclied to it,
and the two together weigh in water 300 grains. Wliat is the
specific gravity of the mahogany \
(18) A piece ( metal weighs 113 grains iu water and 120
grains in air. Wliut is its specific gravity \
(19) A piece of calcareous spar weiglis in air 190 grains
and in water 120 grains. Fhid its specific gravity.
(20) A body weighs 4 oz. in vacuo, ami if another body
which weighs 3 oz. in water be attached to it tlio two together
weigh in water 2j^oz. Find the specific gravity of the former
body.
(21) A piece of wood weighs 12 lbs., and when attached to
22 lbs. of lead and immersed in water the two together weigh
8 lbs. If the specific gravity of lead bo ir35 fintL the specific
gravity of the wood.
(22) If the sinker be equal in magnitude to the substance
wlioso specific gravity is required, but double its weight in
vacuo, and if the two together weighed in water would balance
the sinker in vacuo, wliat is the specific gravity of the sub
stance ?
(23) The specific gravity of cork is 24, and the weight of
a cubic foot of water is 1000 oz.; find the pressure necessary to
he Id down under water a cubic foot of cork.
(24) A cylinder floats vertically in a fluid with S feet of
its length above the fluid; find the whole length of the cylinder,
the specific gravity of the fluid being three times that of the
cylinder.
(25) A cylinder floats with \W\ of its bulk above the surface
of a fluid whose specific gravity is 820, find the specific gravity
of the cylinder.
(26) \yiiy is it easier to swim iu salt water than in fresh \
■
BODIES UNDER THE ACTION OF FLUIDS. 45
(27) Water is ponrcfl into a vcssol containinp; mercury,
rtTid tin iron cylimlor allowed to Hinlc tln*ou.jh i\w water floats
rtith its axis vertieal in Llio mercury. If the cylinder be I inch
in lengtli, lind the lengtli of the portion immonsed in the mer
cury. Tlio spccilic gravity of iron is 7"S, and tliat of mercury
i:j6.
(28) A body, whoso specific gravity is M, floats on water;
if the weight of the l)ody bo lOOO oz., find the number of cubic
inches of it above tlie surface of tlie fluid,
(29) A body containing 12 cubic inches weighs in air 8 lbs.;
deto';uiino its weight in water.
(30) If a cube float on water with one face horizontal, and
a body weighing —  oz., when placed upon it, mai;o it sink
through an inch, tlnd the size of the cube : a cubic foot of water
weighing 1000 oz.
(31) What is the specific gravity of a substance, if a hollow
rectangular box, ten inches long, eight inches wide, six inches
deep, and a quarter of an inch thick, if made of this substance,
will just float in water ?
(32).. A lamina in the form of an equilateral triangle floats
. on a fluid with one of its sides liorizontal and its vertex down
wards. If the density of tlio triangle be onethird that of the
fluid, lind the depth of it vertex below the surface.
(3'Vj , A triangular lamina of uniform tiiickne.^a floats in a
vertical position with its base horizontal and its sides half im
mersed iii a fluid : compare the specific gravity of the lamina
with that of the fluid.
(34) A symmetrical body, weighing 8 lbs,, with a weight
on the top floats just immersed in a fluid: how heavy must the
weight be, in order that, when it is removed, the box may float
with only onethird of it immersed \
(35) Find the specific gravity of a material such that a
cylinder formed of it four inches long floats in water with three
inches immersed.
{^t,'^^ If a cubic foot of water weigh 1000 oz., and a cube
whose edge is 18 inc'u?s weigh 2200 oz., how far will a cylinder
whose length is 3 inches, formed of the same material as tho
cube, sink in water \
i\
:j
I
i*
46 ON riJE CONDITIONS OF EQUIITBRIUM OF
(37) A body, whoso specific fjravity is 27 and weight in
vacuo y lbs., when immersed in a fluid weighs 2 lbs.; find the
specific gravity of the lluid.
(38) The specific gravity of mercury is 13*5 and that of
aluminium is 2*6 ; how deep will a cubic inch of aluminium sink
in a vessel of mercury ?
(39) If a body floats on a fluid twothirds immersed, and
it requires a pressure equivalent to 2 lbs. just to immerse it
totally, what is the weight of the body 1
(40) If a body weighing 3 lbs. floats on a fluid onehalf
immersed, what pressure will sink it completely ?
(41) A piece of cork (s. g. = "24) containing? 2 cubic feet is
kept below water by means of a string fastened to the bottom
of a vessel ; find the tension of the ctring.
(42) Two bodies whoso weights are Wj and w^ in air, weigh
each w in water ; compare their specific gravities.
(43) The cavity in a conical rifle bullet is usually filled
with a plug of some light wood. If the bullet bo held in the
hand beneath the surface of the water, and the plug be then
removed, will the ai)parent weiglit of the bullet be increased
or diminished ?
(44) A body, whose weight in air is 6 lbs., weighs 3 lbs. and
4 lbs. respectively in two diftbrent fluids ; compare the specific
gravities of the fluids.
(45) A body whoso specific gravity is 7'7 and weight in
vacuo 7 lbs., when immersed in a fluid weighs 6 lbs. ; find the
specific gravity of the fluid.
(4G) A solid sphere floats in a fluid with threefourths of
its bulk above the surface : when another s})here half as largo
again is attached to the first by a string, the two S[)heres float
at rest below the surface of tlie fluid ; show that the specific
gravity of quo sphere is G times greater than that of thu
other.
BODIES UNDER THE ACTION OF FLUIDS. 47
(47) « A piece of copper (s. g.^SSo) weighs 887 grains in
water, and 910 grains in alcohol ; find the specific gravity of
the alcohol.
(48) A uniform cylinder, when floating vertically in water,
sinks a depth of 4 inches ; to %vhat depth will it sink in alcohol
of specific gravity 79 ?
(49) « A compound of silver (s. G.= 104) and aluminium
(s. G. = 26) floats half immersed in a vessel of mercury (s. G.=
135). What weight of silver is there in 10 lbs. of the com
pound %
(50) An iron rod weighing 10 lbs. is supported b/ means of
a string, onehalf of the rod being immersed in water. What
force is exerted by the string, the specific gravity of iron being
78?
(.51) A piece of silver weighing 1 oz. in air weighs "905 oz.
in water, what is its specific gravity \
(.52) Two bodies weighing in air 1 and 2 lbs. respectively
are attached to a string passing over a smooth pulley ; the
bodies rest in equilibrium when they are completely immersed
in water. If the si^eciijc gravity of the first body be twice that
of watc;, find the specific gravity of the second.
(63) A cylinder 9 inches in height, specific gravity ^. floats
in water with its axis vertical ; find the height of the surface of
the cylinder above the surface of the water.
Shew that if each division of the stem of the common
(54)
1
hydrometer contains ~th part of tlie bulk of the hydrometer,
the ratio of the specific gravities of two fluids, in which the
hydronieter floats with x and y divisions of the stem out of the
fluid respectively, is equal to my \ mx.
(55) To a body which weighs 3 lbs. in air a piece of lead
which weighs 5 lbs. in air is attached, and the two together
weigh 1;\ lbs. in a fluid whose specific gravity is 4. Find the
specific gravity ofthe body, that of lead being 11.
 (56) ^ A substance weighs 10 oz. in water and 15 oz. in alco
hol, the specific gravity of which is 7947 times that of water :
find the muuber of cubic inches in the substance, taking the
weight of a cubic foot of water as 1000 oz.
J;,
' I
48 ON THE CONDITIONS OF EQUILIBRIUM OF
^ » (57) A block of ice, tho volume of which is a cubic yard,
is observed to float '.vith „^ths of its vohime above tho surface,
and a small piece of granite is ; .en embed<^ed in the ice ; find
the size of the stone, the specific gravities of ice and gi'anite
being respectively '918 and 2'65.
(58) A cubical block of wood weighs 12 lbs. ; the same
bulk of water weighs 320 oz. ; what part of tho wood will be
below the surface when it floats in water ?
(59) A board 3 inches thick sinks 2^ inches in water : what
will a cubic foot of the same wood weigh, if a cubic foot of
water weigii 1000 oz. ?
(60) The specific gravity of beechwood is '85. What por
tion of a cubic foot of that wood will be immersed in sea water
whose specific gravity is r03 %
(61)j A cubical iceberg is 100 feet above the level of tho
sea, its sides being vertical. Given the specific gravity of sea
water=r0263 and of ice = 9214, find the dimensions of the
iceberg,
(62) If a body of weight W float with three quarters of
its volume immersed in fluid, what will be the pressure on a
hand which just keeps it totally immersed ?
(63) > Two hydrometers of the same size and shape float in
two difierCnt fluids with equal portions above the surfaces ; and
the weight of one hydrometer : that of the other \\m \n\ com
pare the specific gravities of the fluids.
^ (64) A hydrometer, loaded with 40 grains, sinks 4 inches
lower when floating in a fluid whose specific gravity is 3 than
in water ; without the weight it rises in the water onetwelfth
of an inch higher : find the weight of the hydrometer.
(65) s If the volume between two successive graduations on
the stem of a hydrometer be yoW^i P^rt of its whole bulk, and
it floats in distilled water with 20 divisions, and in sea watfcr
with 46 divisions, above the surface ; find the specific gravity
of sea water.
{^%) A piece of lead is found to weigh 13 lbs. in water, and
when a block of wood weighing Gibs, is attached to it the two
together weigh 8 lbs. in water. Find the specific gravity of
fchn WftnH
BODIES UNDER THE ACTION OF FLUIDS.
49
(67) What is the weight of a hydrometer which sinks as
deep in rectified spirits, specific gravity '866, as it sinks in water
when loaded with 67 grains ?
(68) ^ Tlse weight of a body A in water of specific gravity
= 1 is 10 oz., of anolhe/ body B in air whose specific gravity
= •0013 is 15 oz.; whUe A and B connected together weigh
11 oz. in walck: shew tllut the specific gravity of B is 10713.
(69) • A substance x^ighs 20 oz. in water and 25 oz. in alco
hol, the specific gvavity of which is '7947 times that of water ;
find the number of c\j6ic inches in the substance, taking the
weight of a cubic foot (f water as 1000 oz.
I
^41
ii ,'
I
y
}
a. n
fifc
CHAFl'ER V.
On the Properties of Air.
\ t.
69. The thin and transparent fluid which surrounds us od
all sides, and which we call the Air or the Atmosphere, is a
material body which possesses weight and resists compression.
We can prove by experiment that even a small mass of air
has an appreciable weight, by exhausting the air from a glass
vessel (by a process which we shall describe in the next
article). We then find that the vessel weighs less than it
weighed before the air was taken out of it.
That the air resists compression is evident from the force
required to drive down the piston of a syringe when the open
end is closed.
'I"
>M
Every body exposed to the atmosphere is subject to a
pressure of nearly \T^ pounds on each square inch of its
surface. We feel no inconvenience from this great pressure,
because the solid parts of our bodies are furnished with incom
pressible fluids, capable of supporting great pressures, while
the hollow parts are filled with air like that which surroimds
us. ^ Also, since the atmosphere acts equally on all iiarts of our
bodies, we have no difiiculty in moving.
\\
ON THE PROPERTIES OF A IK.
5T
70. Hawkslee^s or the common Air Pump.
n
m
ifii
IS a
AB and DEqxq two pistons with valves opening upwards,
which are worked up and down two cylindrical barrels by
means of the toothed wheel W in such a way that one
piston descends as the other ascends. The barrels com
municate, by means of valves at C and F opening upwards,
with a pipe leading into a strong glass vessel V called the
receiver.
Suppose B to be at its lowest position and therefore E at
its highest position. Then as B ascends the valve at B closes,
and the air in the receiver and pipe opens C and expands
itself in the barrel. As soon as B begins to ascend E begins
to descend, the valve at E opens, the valve at F remains
closed.
The air which before occuijied the receiver and pipe, now
occupies the receiver, the pipe, and one of the barrels, and is
therefore rarefied.
Now let the wheel be turned back : then as E ascends the
valve at E closes and F is opened, and meanwhile B is opened
as it descends, and C being closed, a quantity of the rarefied
air is taken from the receiver and pipe.
This process may be continued till the air in the receiver
is so rarefied that it cannot lift the valves at C and F, and
then tJie action of the instrument must cease.
4—2
s»
ON THE PROPERTIES OF AIR,
71. Smeaton^s Air Pump.
A
^v
:b
y
D
AC is a cylindrical barrel communicating with a strong
vesse D called the receiver. At A and C, the ends of the
barrel, are valves opening upwards.
A piston with a valve B opening upwards works up and
down the barrel. Suppose the piston to be in its lowest
position. Then as the piston ascends, the pressure of the air
being removed from the upper surface of the valve at C the
air m DO opens C and expands into the barrel, while' the
valve at B is closed by the pressure of the atmosphere.
Thcis a quantity of air is drawn away from the receiver
As soon as the piston begins to descend, the valve at A is
closed, B opens and C is closed, and no external air comes
mto the barrel or receiver.
When the piston again ascends the air in the barrel i*
ag^ drawn out.
ON THE PROPERTIES OF AIR.
53
The only limit to the exhaustion of the air by this pump
arises from the difficulty in making the piston come into close
contact with the valves at A and G,
Note. The advantage of Smeaton's Air Pump is that since
the valve at A closes as soon as the piston begins to descend
it relieves B from the pressure of the atmosphere, and the
valve at B is opened by a very slight pressure from the air
beneath. Hence this pump is capable of producing a greater
degree of exhaustion than Havvksbee's.
».1
72. To find the density ^of the air in the receiver of
Smeaton's Air Pump after n ascents of the piston.
Let the measures of the capacities of the receiver and the
barrel be respectively x and y.
Then the air which occupied the space whose measure is x
when the piston was at C, will occupy the space whose measure
\%xvy when the piston comes to A^
, density after one ascent _ x
density at first
•I
A.'
^• + 2/
X
:. density after one ascent = ^^^. (density at first).
Similarly,
x
density after second ascent = . (density after one ascent)
and so on ;
.*. density after wth ascent = f j (density at first).
The same formula is applicable to Hawksbee's Air Pump,
if a? represent the measure of the capacity of the receiver and
pipe, and y the iiicasurc of the capacity of eacli of tho barrels.
m
\
*v%\
M
^^
54
^TJIE PROPERTIES OF AIR,
73. The Barometer.
i
ii
of S~u " " '*"™"* '""• """'™""^ '"o P~
end .4, invertli.etah! "t with mercury : if wo then close the
surfaceofthemercnrinf, ? •'«'';'»7 ". the tube from the
e oi tne niercuiy m the basin, is from 28 to 31 inches
atniltett'm'^"rshf™ r"";"^'^" '''■ "'" P— "' 'ho
the receiver ofan air nr,m' t""^ 'l'.' "'^'™""^"' ""^^r
ON THE PROPERTIES OF AIR.
55
74. To shew that the j)i^*issure of the atmosphere is ac
curately rejyresented by the weight oftJie column qf' mercury
in the Barometer.
Take in the surface of the mercury in the basin an area M
equal to the area of the horizontal section of the tube at D.
Then area J/=area of the base of the column of mercury
in the tube, and since tliese areas are equal and in the same
horizontal plane, the pressures on them are equal.
Now pressuvn downwards on J/ — atmospheric pressure on
area M, and i/ressure downwards at Z) = weight of column of
mercury CD.
Therefore the atmospheric pressure on area M is equal to
the weight of the column of mercury CD.
It follows then that the atmospheric pressure on any area
is equal to the weiyht of the column of mercury in the
barometer, having the same area for its base.
Consequently the weight of the column of mercury in the
barometer is tlie proper representative of the pressure of ths
atmosphere on a given surface.
tvl
1
.p.
%
n
t'
f
s«
OAT THE PROPERTIES OF AIR.
7.1. TT(Mico it fulIowH tl.Mt tho height of the column
<if niercmy in tlio biironaitor jh pro i
portioiml to tho prossuro oC tho atmo
sphere.
Tf then wo liiivo a vortical tubo of uni
form boro lillcd up to tho level D with
mercury, if I) bo exposed to tho atmo
splierie proHHuro and if M bo some other
level in tho tubo, and if A bo tho heiht of
the barometric column,
D

U
^^ 
—
prossuro nt /> ^ jvei^j»Uf^c(ju^^ mercury of hrirht h
pressure at M we;ht of a col. ofiiiercu:7«)fheightl/r+^7>J^
h
h + DM'
76. To find the A tmospheric Pressure on a Square Inch.
^ Tho pressure of tho atmosphere on a square inch is dotcr
nnned by frnding tho weiht of a column of mercury ^^■\u,Ro
base IS a square inch and whose height is the samo as the
height of tho colunm of mercury in the barometer.
Taking the specific gravity of mercury as 136, the weight
of a cubic foot of distille<l water as lOOOoz, and the height of
the barometric column at tli. level of the sea as :50 inches, we
have pressure of atmosphere on a square inch
 (^30 X 1 X 1 X —^ X 136 j ounces,
_30x 1000x1.36
1728 xTd '^''"^^«'
• 236^ ounces,
= 14ifif lbs.
OlSr THE PROPERTIES OF AIR.
57
77. In catimiitini? tlio pressnro at a point in tlio interior
of fluid ('xp()H(!(l to the alinoHplicric proHsuro, wo must add
to the p»'essuro on a unit of area contaiiiinj^ tho point tlio
tttmospheric prcssuro on a unit of area.
Supposo for iuHtatico wo have to find tho i)rcHsuro at a
depth of 100 I'eet in a lake, f 1) neglecting atnjospheric pressure,
(2) taking tho atmoHpharic proHHuro into account.
Take a Sijuaro inch aa tho unit of area : then
(1) I'resaure at depth of 100 feet on a square inch
= weight of a column of 'ivater 100 feet in
height, resting on a haso of a square inch
= weight of a column of water whoso cubic
content is (100 x 12 x 1 x 1) cubic inche^j
/I 200 ,, A
(^^^^xlOOOJoz.
lbs.
_ 1200x1000
1728x16'
= 43^ lbs.
(2) Pressure at depth of 100 foot on a square inch
/ 29 \
= f 43 2 + 15] lbs. nearly,
2f)
= 58 r^ lbs. nearly.
78. The Atmosphere is most dense at the surface of the
Earth, and its density diminishes with its height. Hence as
one ascends a mountain tlio weight of tho incumbent air is
diminished, and tho mercury in tho barometer sinks. Thus
the barometer furnishes a means of ascertaining approximately
tho height of a mountain.
7J). a Barometer might be formed with any fluid, but
mercury is preferred to other fluids because of its great
density. A Waterbarometer must have a tube of great
length, since the atmosphere supports a column of water m oro
than 13 times as high as tho colunm of mercury supported in
th(3 uiorcurial barometer.
.^.
w
Hi
»» '
58
ON THE PRO PERT IKS OF AIR.
80. The pressure (if a given quantity of air, at a aiten
temperature, varies inmrsely as the space it occupies.
Tlio following proof by experiment ostablisLes the truth of
tills law.
I ^f ^.'n"". ^'''°*^ *^^''' cylindrical, uniforn. and vertical. The
branch AB is much longer than the branch BC. The ends
uro open. "^
Mercury 18 poured drop by drop into the end A till the
Humice o thc^mercury in the two branches stands at e
same level at P and Q. The end C is then closed.
The« the pressure of air in C(2= the atmospheric pressure.
Let mercury be again poured in at A, (the effect of which
8 to compress the air in CQ,) till the surface of the mercury in
the shorter branch stands at li, halfway between (7 and Q.
uni^V'i^T ^""''^^ *^'^* *^^ "^^^"^^^y "^ <^ho longer branch
r^.ZfnMrMl ""' T""'''^' ''''' '^''^''^ '' thf column of
height of the barometer at the time of making the experiment
ON Tim PROPERTIES OF AIR.
59
Now pressuro at M prcssuro at 7?.
till the
at the
But proMsure at J/= weight of cohiinn of mercury DM
4pro.ssuro of iitmosphcrc ut />,
= atmospheric prcssuro + iitmospherio
IMessure = twieo tho atmospheric
pressure ;
.'. pressure of tho air in CR = twice tho atmospheric pressure.
Hence tho pressure of tho air in CR is twice as gieat as
was tho pressure of the air in VQ.
That is, when tho given quantity of air in CQ has been
compressed into hal/i\\Q space, tiie pressure of tho compressed
air is twice as great as it was at first.
81. Tho proof given in tho preceding Article may bo put
in a more general form, R being any point between (7 and Q,
thus : —
Let mercury bo again poured in at A till tho surface of
tho mercury stands at D and R in the branches, and let M be
level with R.
Then it is found that if tho spaces CQ, CR successively
occupied by tho air bo measured, and if h bo tho height of
tho barometer at the time of performing the experiment,
^m
space CQ, _h + DM
space OR ~ h
Now it is clear by Art. 75,
pressure supporting air in CQ h
pressure supporting air in CR h + DM*
.N
• pregs ufo of air in CQ _ CR
pressure of air in CR ~ CQ'
lii
6o
;■ S
ON THE PROPERTIES OF AIR.
Cor. Flenco r/o can shew that the elastic force of air
varies as its density.
For since the same quantity of air is confined in CQ
and CR ^
density of air in CR : density of air in CQ,
:: Cq : CR
:: pressure of air in CR : pressure of air
'mcq.
82. The Condenstir.
(f
B
^* 'I
»» ■»
^C is a cylindrical barrel with a valve at the bottom, G,
opening downwards into a vessel B, called the receiver. A
piston with a valve A, opening downwards, works in the
barrel.
Suppose the piston to be at the top of the barrel. When
the piston descends, the air in the barrel being condensed
closes the valve at A, and opens the valve at C. Thus the
air which was contained in the barrel is forced into the
receiver. When the piston is raised again, the denser air in
B keeps the valve at C closed, while the pressure of the
atmosphere opens A, and the barrel is refilled with at
mospheric air, wliich is forced into the receiver at tiie next
descent of the piston.
The process may be continued till the required quantity
or air lias been forced into B. * i j
b
P
r
r(
ti
tt
rce of air
ed in CQ
sure of air
ON THE PROPERTIES OF AIR.
ftr
83. To find the density of the air after n descents of the
j)iston.
Let X and y be the measures of capacities of the receiver
and barrel respectively.
Then the air which occupied the space whoso measure is
ic + y, when the piston was at the top of the barrel, will occupy
the space whoso measure is x when the piston comes to the
bottom of the barrel ;
.• density of air in receiver^a^ter onedcscent cc + y
density of air at first "^ ~ ~^ '
.. density of air after one descent = "^"^ •' . (density of air at first).
Similarly,
density after second descent ~^ . (density of air at first)
and so on ; •
•/ density after nth descent = ^,^ . (density of air at first).
I' ii
L
I I
)ttom, (7,
;iver. A
J in the
When
•ndcnsed
'hus the
into the
er air in
of the
vith at
iie next
iuantity
Examples.— V.
(1) If the capacity of the receiver in Smeaton's Air Pump
be ten times that of the barrel, what will be the exhaustion
produced by six strokes of the piston ?
(2) Find the pressure of the air in the receiver of an Air ■
Pump after two strokes of the piston, the volume of the
receiver being eight times t];at of the barrel.
(3) Find the ratio of the volume of the receiver to that of
the barrel in the Air Pump, if at the end of the third stroke
trie density of the air in the receiver : tlie original density
:: 729 : 1000.
•I'
\
» iJ
i ■)
62
ft
i I
ll
OAT THE PROPERTIES OF AIR.
(4) Is it necessary tlnit the section of tlic tube through
wlucli tl.omereiir.yn.es in the barometer should be t]ie same
tnroughout ?
(o) Assuming that a cubic foot of water wcijrhs 1000 02
and a cubic nich of mercury weighs 1% oz, find tlie pressure
on a square inch at a depth of .90 feet below the surface of the
sea, when the barometer stands at 30 inches.
in f^' \?''f y ^^•'' ''''*'^" '''^ ^''^^ '^^''^^" '''^^ barometer bo
10 times that o a section of tlic tube, and the mercury fall 1^
inches in the txxh^,, Hnd the true variation in the height of the
mercury, and draw a figure reivfesenting the instrument.
?i 1 ^\^ ^''^^ '''"''' '"^'^^ ^" *^'^ ^"^^ of •'^ barometer, what
would be the effect ? , rtt
(8) If the weight of the column of mercury which is above
the exposed surfiice in a barometer be an ounce, and the area
of the transverse section of the tube ^ of a square inch, what
is the pressure of the atmospliero on a square inch?
(9) When the mercurial barotneter stands at 30 inches
what wdlbe the height of the column in a barometer filled
with a fluid of specific gravity 34, the specific gravity of mer
cury being 136?
T..^T,^ ^^'■^^"^^^^^' ^^i" it have any effect on the indica
tion of the instrument?
(11) If a body were floating on a fluid, with which the air'
was m contact, and the air were suddenly removed, would tlip
body rise or sink in the fluid ? '
^ (12) What would be the eflfect of admitting a little air
into the upper part of the tube of the Barometer ?
(13) A pipe carries rain water from the top of a house to
a aigc tank, the surplus water in which escapes throuoj, a
valve in the top which rises freely. A weight of 21 lb is
placed on it and it is found that tiie water rises in the pipe
to tlie height of 20 feet before the val r.pons. Find its area
assuming that the height of the Water Barometer is 34 feet'
Rnd the atmospheric pressure 15 lbs. on the square inch.
/.
IR.
tube through
' be tJie same
?ighs 1000 02.
the pressure
mrface of tlie
•urometer bo
3rcurv fall \\
loight of the
umeiit.
meter, what
rich is above
md the area
e inch, what
I?
' 30 inches,
neter filled
'ity of nier
ontained in
the indica
lich the air"
would the
1 little air
a house to
througli a
■ 21 lbs is
n the pipe
id its area,
is 34 feet
iich.
ON THE PROPERTIL:, OF AiK.
^l
(14) A cylinder filled with atnios])]icric air, and closed by
an airtiglit piston, is sunk to the depth of 500 fathoms in the
sea; required the compression of the air, assuming the specific
gravity cf sea water to be ro27, tiie specific gravity of mercury
13"57j and the height of tiio barometer ;50 inches.
05) A barometer is sunk to the deptli of 20 feet in a
Like: find the consequent rise in the mercurial column, the
specific gravity of mercury being 13 '5 7.
(16) If a body, exposed to the pressure of the air, float in
water, prove that it will rise very slightly out of the water as
the barometer rises, and sink a little deeper as the barometer
fiills.
(17) V Water floats on mercury to the depth of 17 feet,
compare the atmospheric pressure with the pressure at a point
15 inclics below the rirface of the mercury, takhig into ac
count the atmospheric pressure on the surface of the water,
having given that the heights of the mercurial and water
barometers are 30 inches and 34 feet iespectively.
(18) Explain clearly why a balloon ascends.
(19) Explain how it is that a bladder filled with air, will,
if conveyed deep enough in the sea, sink to the bottom.
(20) What would be the height of the column of mercury
(s. G.= ].T5G) corresponding to a pressure of 14 lbs. 2 oz. on
the square inch \
(21) .A cubical vessel full of air, whoso edge equals n
inches, is closed by a weightless piston. Find the number of
pounds which must be pl;ced on the piston in order that it
may rest in equilibrium at a distance of 2 inches from tlie
bottom of the vessel : the [ircssurc of tiie atmosphere being
15 lbs. on a square inch.
(22) The lower valve of a pump is 30 feet 4 inches above
the surface of the wat r to be raised : lind the height of the
barouioter wlien the pump ceases to work, the specilic gravity
of mercury being 13'6.
,i»'!
■^
64
ON THE PROPERTIES OF AIR.
(23) It IS found that the cork of a bottle is just driven out
when the pressure .f tiio air svithin is double that without • tho
bottle IS then filled with mercury i.nd inverted, and it is a'ain
iound that tlie cork is just driven out. Given that °the
barometer was standing at 30 inches at the time, find the
height of the bottle.
I
I
* r i 1 . ^^'^ ''^*^''' ^^ *^'^ ^'o^^^'"e Of the receiver to that
of the barrel m a Condenser, if at the end of the tliird stroke
the density of the air in the receiver : its original density
^ (25) A hollow cylinder closed at tho upper end and open
at the lower is depressed from the atmosphere into water, its
axis being kept vertical, and is found to float with its upper
end in the surface of the water. Wluat will be the effect on
tlie cylinder of an increase of atmospheric pressure ?
cJ'^^l ^^ ^'"^ ''""^''"''^ ^^ *^'® cylinder in a Condenser be one
fifth tne vo ume of the receiver, find the pressure at any
point oi the latter after 20 strokes. '
(27) The pressure at the bottom of a well is double that
at Che depth of a foot; what is the depth of the well if the
pressure of the atmosphere be equivalent to 30 feet of water ?
(28) A cubic foot of water weighs 1000 oz. ; what will be
the pressure on each souare inch of the base of a cube whose
edges are 10 inches, when filled with water ?
1 '<
(29) A cubic foot of water weighs 1000 ounces, and the
pressure of the air on a square inch is 236 omices ; find the
pressure on 16 square inches at a depth of 9 feet below tho
suriace of a pond.
(30)' If4^, C, be three points in a uniform fluid at rc^t
the three points being in the same vertical line, and tho dif
ference of the pressures at A and ^: difterence of the pres
sures at A and C as ;> : q, find the ratio of AB to BG.
(31) Explain the princ'ii)!e of the Airgun.
ON JN/i PROPFRTIT'S ( ^ AIR.
driven out
:.Iaout ; tho
it is again
that the
, find tlie
3r to tliat
rd stroke
! density
and open
vater, its
its npper
effect on
be one
at any
ible that
il if the
water ?
65
< (32)« If tho area of tlie basin of a barometer be 17 times
that of a section of the tube, how ought tlie si cm to bo gradu
ated in order that the reading may give the true height of the
barometer ?
(33) If the specific gravity of mercury be 13*57, and the
weight of a cubic inch of water 252G grains, find tlie pressuro
of the air on a square incli in lbs., when the mercury in the
barometer stands at 30'5 inches.
• (34) . If the tube of a barometen be 36 inches long, and, on
account of air being in the upper part, the instrument stands
at 27 inches, when a correct instrument stands at 30 inches,
what length of tube would the air fill when reduced to atmo
spheric density ?
(35) The specific gravity ot the weights employed by
jewellers, for weighing i)reci()us stones, is greater th .11 that of
the stones themselves. Is it more advantageous for the jeweller
to sell stones when the barometer is high, or when it is low ?
(36) f A tube closed at both ends and 2S inches long is half
filled with mercury, the remaining portion being occupied with
air at atmospheric pressure. If the tube be placed in a verti
cal position with the mercury uppermost, and the upper end
be opened, find how fiir the mercury will sink, the height of tho
barometer at the time bein^ 28 inches.
:i
t will be
e whose
% i
and the
find the
;low tho
at rc^t,
tho dif
prea
i
Nil
&H.
J*
1 1 '
CHAn'ER VI.
On the Application oj /ifr.
^\ Tlie Diving Bell.
i\
' I
,0^
>■*■■
>•
if
i
4
.IJ
If a glass be inverted, and witli its month horizontal be
pressed down into a basin of water, it will be seen that though
some portion of water ascends into the glass, the greater part
of the glass is without w^'^tcr.
This is caused by the Cdmpressionof the air, which prevents
the water from rising in tlie glass.
The Diving Bell works on the same principle. A heavy
iron chest BCED, open at DE, is suspended from a rope A,
and lowered into the water, with its open end downwards.
The water will then rise till the air in the chest is sufficiently
compressed to prevent the water from rising beyond a certain
height MN.
Air is pumped in occasitmally through a pi] to /', and the
impure air is allowed to escape through :uiother piv ' Q.
■"'^*.
ON THE APPLICATION OF AIR.
67
>sft. The Common or Suction Pump.
1*
I)
I
Al
ABh'A cylindrical barrel in which a piston P, withavalvo
opening upwards, is worked up and down by the handle R.
ItCiH a pipe, conimunioating with the barrel by u valve, oi)en
ing upwards. The end C, which is pierced with ii number of
small holes, is placed under the surface of the water which is
to be raised.
Suppose the piston to be at the bottom of tlie barrel.
Then when the piston is raised the valve P is closed by the
pressure of the iiir on its upper surface, r.iid tlicie being
little or no air in PB, the valve B is opened by the action
of the air in BC, and as it continues open during tJie whole as
cent of the piston, the air in BIl, the part of the suctitmpipe
above the surface of the water, expands into the barrel, and
becomes less dense than the air which presses on the water
v>utsido the sucti()ii[)ipe. The water is consequently forced up
the pipe by the i)ressurc of tiie atmosphere, till the pressure
downwards at 1/ is equal to the atmos)lieric pressure.
When the piston descends the valve B closes, and the air
m PB, being condensed, opens the valve P.
This process being continued, the water will at length rise
through the valve B, and at the next ascent of the piston a
mass of wat'T v'U be lifted and discharged tlu'ough the
sp^'Ut D.
•t 1
6S
0!f Tim AITUCATION OF AIR.
0. '^l^t^^T" "i" '■■" "^"ci«i.tofacoi;;;;;;
86. TJie Forcing Pump.
1^1
'• .
o .\L'
^^ is a cylindriuil barrel in whic. u solid piston P ia
worked up and down the space AF.
BGh a suctionpipe of whtcli the end is placed under
the surface of the water.
BE is a [)ipe communicating with the bairel.
At B and Z> arc valves opening upwards.
Suppose the piston to be at the bottom of its range in the
barrel. Then when the piston is raised the valve at D remains
ON THE AITUCATION OF AIR.
69
closed, tho air in Z>/?/^ expands as the piston rises, and tlio air
in BII opens tlic valve B and expands into tho barrel. Tho
water is tliercfoi'O forced up tlio suctionpipe by the pressui'e
of tlio atmosphere.
When tho piston descends the air in PFBD is condensed,
closes the valve B, opens tho valve i>, and escapes through Z>.
When the piston ascends again the water rises higher in
BG, and this process is continued till tho water rises through
B. Thou tho piston on its descent forces tho water up the
pipe DE.
•«')
87. In order to produce a continuous stream through the
pipe at E, the pipe is Introduced into an airtight vessel Dll
into which the valve D opens.
JE
/
^
I
•^v^i^i^^^.
etI"^
~o. z
=£^!yizf
D
r*" —
re«
" "
u^ — 1

1
i
v
— 1
1
A
en
'11
J
When the water has been forced into this vessel till it rises
above 0, the lower end of the pipe, the air which lies between
the surface of the water in the vessel and the top of tiie vessel
is suddenly condensed at each stroke of the piston, and by its
reaction on the water forces it through the pipe OE in a con
tinuous stream.
wf
70
I
I
!l
I
'i
'H
8S. T/w riro Enfjlue.
Tliis macliino consists of a donl,l„ t ■
r«.«ps co„„„„,.icati„g ,vith thesatatvcre'ri;''"'"''' """"
T1.0 pipe r dcccnd. into a .■c.,,e,voh. of natcr '
n.o valves opening „p,vards are at F, F ,, ,, ^ ^
^^..s a fixed beau, round ,v,,iol. the pi.,tu,rods Jork
' '" ''""■•'' '" '''=«''« '■S'^d llirougi, the pipe //.
ON THE APPfJCATIOiV OF AIR.
7<
S.'». The LijVmg Pump.
^r
H
W:
AB is a cylindrical barrel in which a piston with a valve J/
openin<^ upwards works, the piston rod passing through an air
tight collar at A.
BO is the suctionpipe of which the end G is placed under
the surface of the water.
DE is a [)ipo up which the water is to be raised.
At D and B arc valves o[)ening upwards.
The water will be brought within reach of the piston by a
process similiir to that which has been described in the case of
the other piuups.
When le piston nscends lifting water the valve at Z) opens,
and the water is discharged into the pipe DE. When the
piston descends, the valve at D closes, and prevents the return
of tlio water in DE into the barrel. ».
Each stroke of the piston increases the quantity of water in
DE, and thus the water may be niiscd to any hciglit, provided
that the barrel AB, the pipe ED, and the piston rod be strong
enough to bear the pressure of the superincunibout column of
rrater.
m
u
t ; ^
.. t
7a
^^ Tim APPLICATION OF
AIR.
90. The Siphon.
»ipi,ri:; y;,"!!!'' ^ '"» "•'« ^f^ .. th., .ra„e,.„: of ti,o
P»i"t of the ».>ho,iltf,i' rr''""' 1'"" ^' "'0 '"Shest
of the fluid : thei " "^*''" "'''''°"' "' "'o ™rface
pressure of atmosphere at //i„ dircctio,. ^5 = pres,„re
on area Z),
pressure of atmosphere at ^'in direetion (7Z? = pre,.„re
on area Z>,
••• pressure of atasphere at //i„ direction /«=press«re
of atmo«phcro at C in direction CB
4rof''c'ir of«:inrLi/ ■' *'r'^"<"' "^ "•«
o^. dimi,,.,hea h. the weif^fro/r rfl:[;Sar
ON THE APPJJCATJOh' OF A IP,
73
fcho column liC h proator than ((.liunn /?//; tlio cfTectlvi', pro;
8uro of ittniosphoru in direcl.ioii ///
prossuro of atnio.spliero in di
will bo driven by tho elYuutivu atnio.^plicric prcsHuro iu a cou
tinuous streuui iu tho Uirootiuu UBC.
'j is <,^rtMter tlian i\w ell eel Ice
I
91. On intennitling ^j^rings.
rnteruiitting Springs arc springs which run for a time, then
Ptop for a tinio, aud then begin to ruu again.
This phenomenon is explained by tho priuciplo of tho
Siphon.
Lot A bo a reservoir in a hill in which water is gradually
collected through fissures, as B, C, Z>, communicating with tho
external air.
A
Now suppose a channel MNR to run from A, first ascend
ing to N and then descending to R, a place lower than tho
reservoir.
As the water collects in A it gradually rises in the channel
to iV, and then flows along NR, and by the principle of the
Siphon it will continue to H'vv till A is completely drained.
Then the flow ceases till the water in A has collected suflicient
ly to reach N.
■4^
f .
t ■
\
7^
OJV THE APPLICA TION OF AIR.
92. Bramah's Press.
Tho^ Hydrostatic Press, generally called Braniah's Press, is
a machine by which an enormous pressure is obtained by means
of water, tiie only assicrnabio limits to its power being the
strength of the materials of which it is formed.
^ ^ C is a forcingpump, by the action of which water is forced
mto a tube BD, which has a valve B opening inwards.
^ is a strong cylindrical piston, with a base many times
larger than t!ie base of the piston A, working in a vvaterti«ht
collar at M, N. "
111 P
Between the top of the piston E and a fixed beam FG, a
bale of goods, such as paper, cotton or wool, is placed.
Suppose the area of the base of E to bo 200 times that of
the base of ^.
Then if a pressure of 100 lbs. be applied to A, a pressure of
(200 X 100) lbs. or 20,000 lbs. will be conveyed to the base of E.
ihus any amount of pressure may be applied fo JV, eHlier
by mcreasing the pressure applied to A, or by making the base
Qt ^ larger m comparison vvitl) the base of A.
UN THE APPLICATION OF AIR.
75
s Press, is
by means
the
being
r is forced
s.
my times
atertig!)t
nFG,a.
3 that of
(ssure of
so of E.
^, either
the base
Examples. — VI.
(1) What will be the clfcct of making a small aperture in
the barrel of a Forcing Pump ? If the piston work uniformly
up and down the length of the barrel, and a small aperture be
made one third of tiic way up the burrel, how much more time
than before will bo consumed in filling a tank i
(2) If t!io upward motion of the piston of a Common
Pump be stopped, when the water has risen to the height of
16 feet in the supply pipe, but has not yet reached the piston,
find the tension of the pistonrod, the area of the piston being
4 square inches, and the atmospheric pressure 15 lbs. on the
square inch.
(3) What would be the efifect of opening a small hole at
any {Mjint in the Siphon, first above, secondly below the surface
of the fluid in the vessel ?
(4) What is the greatest height above the surface of a
spring over which its water may be carried by means of a
siphontube, when the barometer stands at 29 inches, the
Bpocific gravity of mercury being 1;JT)7 ?
(5) What would take place in a siphon at work if the
pressure of the atmosphere were removed 1
(G) ^Vill the siphon act better at the top or the bottom of
a mountain ?
(7) Could a siphon be emploj'ed to pump water out of the
hold of a sliip floating in a harbour I
(8) What is the gr(;atest height over which water can be
carried by means of a siphon when the mercurial barometer
stands at 30 inches ?
(9) If the ends of a siphon were immersed in two fluids of
the same kind and the air were removed, describe what would
take place.
(10) A ii'jUow tube is introduced into the bottom of a
cylindrical vessel through un airtight collar ; and a large tube,
of v/hich the top is closed, supeuded over it, so as not quite to
touch the bottom : consider the effect of gradually pouring
water into the cylinder, until it reaches the level of the top of
tl)0 iiivertod tube.
:<i ' '
4
•
m
ill
^
t >
ii
•I

76
OJV THE APPLICATION OF A JR.
(11) A siphon i,s placed with one end in a vessel full of
water, and the other in a similar empty one, both of which are
on the plate of an airpump. As soon as the water has cover
ed the lower end of the siphon, a receiver is put on, and the
air rapidly exhausted, and then gradually readmitted : describe
the effects produced.
(12) A siphon, filled with water, has its ends inserted in
vessels filled with water ; state what will take place when the
vertical distances of the highest point of tlie siphon above the
surface of the fluid are both less, both greater, and one greater
and the other loss than the height of the WaterBarometer.
(13) What is the length of the smallest siphon that cas
empty a vessel 2 feet deep 1
*« f
. i
ssel full of
which aro
has covcr
11, and tho
: describe
nserted in
when the
abovo the
nc greater
)mcter.
1 that cas
CHAPTER VII,
On the Therinometet,
93. The general consequence of imparting heat to bodies
is the expansion of their volume.
The particles which compose a solid body, as for instance a
block of lead, are hold together by tho force of cohesion. It
requires a force of great magnitude to increase or to decrease
the volume of a block of lead, though lead is a soft metal.
The ai)plication of iieat, by we ikening the force of cohesion,
reduces lead and other metals to a liquid state, pushes the
particles more widely apart, and thus increases the volume of
the bodies to which it is applied.
If heat be applied to a liquid, as water, the cohesion of the
particles is weakened, and they nltimately acquire a tendency
to break away from each other and assume the form of a
vapour.
If heat be applied to an elastic fluid, as air, it
causes it to expand. Thus if a bladder, partly full
of air, be placeil before a fire, the air will expand
and distend the bladder.
Again, if a piston P exactly fits a cylindrical
tube AB, and is supported by the condensed air
ia PB, if heat bo ai)i)lied to the air in PB it will
expand and raise tho piston.
78
ON THE THERMOMETER.
.♦i
1 '»\
.ft I
closed ".T'^'f f;"'"''.™ '"'" "f ""''■<"■"> •«»°
ha b ,lh 'ri'"'; ''•''■"""■■""'S at «'<•■ other end
0.1 nu'f ,,''"''"""'""*'"'» "'"■•oury, whicl, ex
betwci; M,„ '™^ ",'' ""' "•''^■ ■J'l"> »I«ce
vaaram "■""''^ """^ "'« '"l* "f""' ""'« «a
If Oic mercury i„ the iiistrmiuuit bo subiectod
tnhfhT'^M "' ""''^'"""^ "^ the upper part of the
tube before the end A is closed by n akipc. the
95. 7>) j7m^?^Yri^ « Thermometer.
descends and fin.ilv becmn',. «? * '^ ""™'''^' "'« «'''"™
it rests is .narkod t r tl,f ;''""^ '^'"■' P""" ^^ ''I™''
momoter. "'^ '''■'''■*"''' P"'"' "f the ther
in. nl::i;;t~^,:<^: ™ the :r ^ ^ ™ ^o"
the cohiMin rises and fino v 1 J tlie mercury expands,
wi.ich it rests iT, aH.ed ^ ^Zt 7 '""'^ ^'^^ ^^"^^ '^
mometer. ' ''^'' ^'"''^'^'^ ^^^^^^ of the tlier
The space between thr free^inf^ nninf o,. i n u •,•
is divided into cq,ud spaces, 0.11:;°^" "'"= """"
and'b„S;n;;7i",fe,Iir™'''"'''''^f'^^'"S ""t is n>arkcd 32«
boili;;» "oo! ''"''™'^'»«"^ freezing pointis .uarkcd 0« and
114 ! 8
96. Haol
tig gi':cn the viavhcr of degrei
TJiermometer^ to p,d the coZZ ;^"^'''"" ^^ P^hrerheif.
ontheCentia^ad/^hJZ:::::^'''^'''^ ''^''^^'^ of degrees
liiennoineter.
lunent con
i extent of
ON THE THERMOMETER.
7V
Let AM be the line at which the mercury stands at freezing
point,
BN at boiling point.
100 ■
JB
N
d
212
2P'
32^
m
i leaves a
lorcury is
e column
at which
the thei
iter boil
cxptinds,
3 point at
ho tlier
ing point
marked
"ked 32"^
d 0" and
degrees
Then
AM and BN are marked 0" and 100" on the Centigrade scale
32*^ and 212" Fahrenheit
Let the mercury stand at the line PQ^ and suppose the
graduations on the sl Jes ^^ be C^ and F'^ respectively.
. AP MQ
^''''ab^mn^
or
C
F 32
100 2J232'
C_ _i^32
*^^106~ 180 '
C_i^32
•*• 5 " 9 '
and from this equation we can find G when F is given and /'
when C is given.
97. To compare the scales of the Centigrade and Reau
mur's Thermometer, we proceed hi the same way, putting ^0"
R, W instead of 32", i^, 212*^ respectively, and we obtain
G _R
100 ~ bO '
G R
or  =  .
o 4
Hence the three scales are thus connected,
C F 32 R
5
9
8o
ON THE THERMOMETER.
f) V
li;
Pifi
IfL ,
li.M* 1
ii^ i
111 \
[lli
If'
98. The following examples will sliowl^ow to findTtlu.
number of de^^reos marked on any one of the three eales tl n
the number marked on one of tiie other scales is given
Since ^=^32
5 9 '
andi^=5fj,
C_ 5632
5 9 ~ '
.'. 9C=5x24,
.'. the reading on the Centigrade scale is 13^ degrees.
to ^^^^r^"^ ''' Fahrenheit scale correspond.
bince C= 14,
14 ^ i>'32
5'~ 9 '
.M26 = 5/'^160,
.. 52'"= 28G,
that is, the reading on the Fahrenheit scale is 57 1".
E:?. (3) If the sum of the readings on a Centigrade anu a
Reaumur be 90, what is the reading on each ?
and'^'*' '''' ^'^""^ *''''' equations, from which we can fina (
C H
5=4 (1^'
(7+72 = 90 (2);
.. 4C=5i2 I
4(7+ 4/2 =.360 J '
.. 4/.» = 3605iif,
'. 9i2 = 360,
andsoi2 = 40aiid o'=50.
Ill
I P
ON THE THERMOMETER.
81
find tilt!
:iles when
sn.
!e cor
TU
3es.
esponds
! anil ii
find (
Examples.— VII.
(1) Givo tliG number of dcgiees in tlio Centigrade and
Reaumur's scale respectively that correspond to the following
readings on Fahrenheit's scale,
(1) 30", (2) 45«, (3) 56% (4) 0«, (5) 7", (6) 45°.
(2) Give the number of degrees in the Centigrade and
Fahrenheit's scale respectively that correspond to the following
readings on Reaumur's scale,
(1) 50, (2) 20'>, (3) 0", (4) 18«, (5) 64% (6) 120%
(3) Give the number of degrees in Fahrenheit's and
Reaumur's scales respectively that correspond to the following
readings on the Centigrade scale,
(1) 16% (2) 45% (3) 110% (4) 0% (5) 15% (6) 24«.
(4) Is it necessary that the section of the tube through
which the mercury rises in the Thermometer should be the
same throughout ?
(5) If the sum of the readings on a Centigrade and Fahren
heit be 60, Avhat is the reading on each ?
(G) At what temperature will the degrees on Fahrenheit
bo five times as great as the corresponding degrees on the
Centigrade ?
(7) At what point do Fahrenheit on. ' the Centigi'ade mark
the same number of degrees ?
(8) Show how to graduate a Thermometer on whose scale
20° shall denote the freezhig pohit, and whose 80th degree shall
indicate the same temperature as SO" Fahrenheit.
(9) What will bo the reading on the Centigrade when
Fahrenheit stands at 78" I
(10) The sum of the number of degrees indicating the
same temperature on the '^^witigrado and Fahrenheit is 88,
find the number of degrees oi« each.
(11) What readin,? on the Centigrade corresponds to 49»
Fahreiibcit 1
p. n. ®
i!^
•I
i'.i;
•ii
ill
m
m
8.
i! ,U.
M
'» I %
(9/V yy/A' THERMOMETER,
o limes as fcrut as the corresponding degrees Centigrade !
10»^' ™.U,»r ™'™""<'''" ''""ks t»o temperatures by9«a,Kl
^o»rLtLT';^;:irt'•^'t^!::?l::"';r^
mark when the former marks le"? ' "'" """""'"•
c.ease h, a given" tlmL'eVo d^ ^ 'find ho': mT", "'■
the tliormometers has risen. ' ' """'' <""='' «'
\'
\'
CHAPTER Vin.
Miscellaneous Examples.
99. We shall now give a series of examples to illustrate
more fully the principles explained in the preceding Chapters.
The important law of pressure in the case of compressed air,
of which v:e treated in Arts. 80, 81, will be referred to as
MarrioU&'s Law *.
Examples worked out.
1. Water is 770 thnes as lieavy as air. At what depth
I in a lake 'tcould a bubble of air be compressed to the density
' of 2oater, supposing Marriotte's law to hold good throughout
tor compression?
At the surface the density = that of ainiosphore,
and 33 feet of water are equivalent to one atmosphere ;
.'. at depth of 33 ft. the density = twice atmospheric pressure,
(2 X 33) ft = three times
(769x33)ft = 770times
/. the density will be equal to that of water at a depth of
(769 X 33) ft. i. e., '2i>371 ft.
• It was proved by the independent researches of Marriotte, a French
Physician, and Boyle, the Enpli»K Philosopher.
6—2
f
84
,' f
n ,»
'I
i
If
MIS CELLANEO US EXAMPLES.
2. A body weighs in air iomnrs in wniAr mn .»..» Z
In water tlio body lose, (l 000  300) grs.. /. 0, 700 grs
in other liquid /j^^,. ,,,., . '
.'. equal v..lt]me.s of water and of thn nth.,^ 1; • 1
«pectively 700 grs. and 5.0 gr" " ^"^'"^ ^^'^'^^^ ^^
•■• "^°^^^»'*^ «f «P^cinr gravity of other liquid = ''^^ = 6^857] i.
in^aMe u the pressure tmce what it is at a depth of on.
Pressure at tlio surface = weight of column of wnter 33 ft. hi^h
..for a double pressure we must take 3(5 feet lower thatis
3b teet lower than 3 feet, or 39 feet from the surface '
4. A Jlat piece of iron, ^,:eicjhiug 3 lhs.,fiuats in mercury;
and if another piece of iron of like density iceiyhing 2 1. lbs.'
is placed upon it, the j nece is just immersed. CoLara
the ,pecijic gravities of t. ^ and mercury. Compare
Total weight of iron = (sf 2 . ) lbs. = .5 ^ lbs.
Tlie volumes of the part immersed and of the whole will be
as the weights, that is, as 3 : 5 A ^ or as 78 : 135.
.'. 8p.gr. of iron : sp. gr. of mercury = 78 : 135,
= 2() ; 45.
5. Air is confined in a cylinder surmounted hy a piston
without rcnght ^^.hose area is a square foot. What S
must he placed on the pi.ton thai the volume of air Zy I
reduced to half its dimensions? ^
will^hafe'dtble'ilr "• ' '^J' ^^''^'" '''^''''^ '' ^'^^ '^'' ^'^^'^
will lla^e double its original pressure. Hence takin 15 lbs
per square meh as the original atmospheric pressure, it be.*
MISCELLANEOUS EXAMPLES.
^5
i
comes 30 lbs. per siintiro incli below the piston. But the ut
niosphero still exerts a pressure of If) lbs. i)er squiire inch
above the piston. Therefore a pressure of in lbs. moro per
square inch is required to keep the ])iston at rest.
/. weight requircd=(15 x 144) lbs. = 21G0 lbs.
6 If the mpacitf/ of the receiver of an airpump he 10
ti?nc,s that of the barrel, sheic thai, after n strokes of the pistoji,
the air in the receiver will have lost nearly onefoarth of its
density.
By the forn ^a of Art. 72, if po ^i'^^ Pn bo the densities
originally and alter the m^'' stroke, and R and B be tlio capa
cities of the receiver and barrel,
Po
P3
Po
D„ _ / R \n
/_u)_Y^iooo,
VlO+ V ~ 1331'
,. density lost = (l  ^^j po= ^^Po = ^Po nearly.
7. A block of wood( s. G. "j loclghing 156 lbs. is float
ing in fresh water. What weight placed on it will sink it to
the level of the water ?
Let x = \X\Q weight in lbs.
Then x v 156=weiht in lbs. of water displaced by volume
of wood alone,
13 ._
= 169;
.*. ^^(169156) lbs. = 13 lbs.
8. In a mixture of two fluids, of ichich the specific gra
vities are 3 and 5 respectively, a body, whose s. g. is 8, lo&es
half its weight. Compare the volumes mixed.
Weight lost = weight of fluid displaced,
= ^ weight of body whose s. G. is 8,
:, S. G. of the uaxture is 4.
^a^
IMAGE EVALUATiON
TEST TARGET (MT3)
1.0
I.I
1.25
■ IIIIIM
50 '""^=
;i' m
M
2.0
1.4 ill 1.6
6"
P>2
;^
<P» Am..
V.
Photographic
Sciences
Corporation
23 WEST MAIN STREET
WEBSTER, N.Y. 14580
(716) 8/24503
<^
iV
M
^
A
\
ls!.<
I . I
. ::r
'I : I
86
MISCELLANEOUS EXAMPLES.
9. ^4 ^•^6•*^<? r/ «^a^^r A^^ for its horizontal section a rect
angle 6 feet hy 2 feet. A substance ^ceighing 550 Ihs is im.
mersed in U, and the water rises 8 inches. Find the specTtic
ramty of the substance. ^ ^
Sectional area = 1 2 square feet.
Volume of substance = ( 12 x ?) cub. ft.
= 8 cubic feet ;
.\ 8 cubic feet of the substance weigh 550 lbs. •
550
.'. 1 cub. ft.
8
lbs., or 6875 lbs.
Also, a cubic foot of water weighs 625 lbs.,
.. sp. gr. of substance =. ^^ ^ii
10. A cylinder floats in a fluid A with onethird of its
axis immersed, and in another B with three fo7irths of its
Mixture ofequcd columes of A and B?
Sp. gr. of^ : s). gr. of ^ =
4
= })
1
3'
4;
.*. sp. gr. of mixture of equal volumes = ^ = 65.
If therefore the body has \ of its axis immersed in a fluid
of S.G. 9 when it is immersed in a fluid of s.a 65 the mrt
immersed is obtained from the following relation, where ^ is
the part immersed,
9 X
t)
X.
1
6
13
MISCELLANEOUS EXAMPLES.
87
100. We shall now give a sot of easy Examples to bo
vrorkcd by the student by way of practice.
Examples. — VIII.
1. An iceberg (s. G. 925) floats in seawater (s.g. 1'025).
Find the ratio of the part out of the water to the part im
mersed.
2. . A body floats in a fluid (s. g. 9) with as much of its
volume out of the fluid as would be innncrscd if it floated in a
fluid (s. G. ri). Find the specific gravity of the body.
3. Find the Fahrenheit Temperatures corresponding to
40" and 43r)0'' Centigrade.
4. The capacities of the barrel and receiver in a Smea
ton's airpump are as 1 : 3. A barometer enclosed in tho
receiver stands at 28 inches. What will be the height after
three upward strokes of the piston ]
5. Two hydrometers of the same size and shape float in
two different fluids with equal portions above the surfaces, and
the weight of one hydrometer : that of the other = 1 ; ??.
Compare the specific gravities of the fluids.
6. A man weighing 10 stone 10 cz. floats with the water
up to his chin when he has a bladder under each arm ecpud in
size to his head and without weight. If his liead be one
twelfth of his whole bulk, find his specific gravity.
7 At what height does the water barometer stand when
the mercurial barometer stands at 28 inches (s.g. of mercury
=136)?
8. What degree Centigrade corresponds to 27'' Fahren
hei;. ?
9 A man G*feet high dives vertically downwards with hia
hands stretched 18 inches beyond his head. What depth has
ho reached when the pressure at his fingers' ends is .^ that at
hia feoti
t
8S
MISCELLANEOm EXAMPLES.
I .
P: 'J
ir
S it
■Si
^ :^
' (
10. . A stringf will bear a strain of 10 lbs. 7 oz. Dotor.'iiine
the size of the largest ricco of corii (s. g. 21) wliich it can keep
below the surface of mercury (s. g. 136).
11. In De Lisle's Thermometer the freezing point is 150"
and the boiling point zero. What degree of this thermometer
corresponds to 47" Fahrenheit?
12. Cork would float in n atmospheres. Find n (s g of
air and cork being 0013 and 24}.
13. An elastic body of s. g. "5 is compressed to ^^ of
20 + 4>i
its natural size by immersion 7i feet in Tvater. At what depth
will it rest? ^
14. If the body in Question 13 weigh lOlbs., what are tho
magnitudes and directions of the forces which will keep it in
equilibrium at deptlis (a) 5 feet, and {(i) 30 feetr
15. At what depths will the force required to keep the
body in Questions 13 and 14 at rest be 1 lb. ?
16. At what temperature are the readings on Reaumur.
Centigrade and Fahrenheit proportional to 4, 5, 25 ?
17. At what temperature is the sum of the readings on
Keaumur, Centigrade and Fahrenheit 212 1
18. A body (s.G. 26) weighs 22 lbs. in vacuo and another
body (s. G. 78) weighs n\U. in vacuo; and their apparent
weights in water are equal. Find n.
19. Find the specific gravity of the fluid in which the
apparent weights of 1 lb. of one substance (s. g. 3) and 3 lbs. of
another substance (s. g. 2 25) are equal.
20. Equal volumes of two substances (s. g. 27 and 61 > are
immersed in water and balance on a straight lever 71 inches
ong. Find the position of the fulcrum.
,. J^^' ^^^ proceed witli some examples of somewhat greater
difhculty than those already given.
Note. We shall assume that the volume of a sphere Is
.rrrr^, r being the radius
MISCELLANEOUS EXAMPLE^.
89
Dotcrniine
b can keep
int is 150"
rmomoter
n (s. Q. of
20 + w
tiat deptli
it are tlie
icep it in
keep the
leaumur.
dings on
another
ipparent
liich the
3 lbs. of
6*1) are
1 inches
greater
)here is
Examples worked out.
1. Shew how the deplh of the descent in a Dimng Bell
can he determined from ohservalions on the barometer.
A H
y
D
Let AB be the surface of the water, CD the water level in
the bell at the end of the descent.
Now pressure at CD is equal to pressure throughout the
upper part of the bell, and is therefore equal to the pressure
due to atmosphere 1 weight of column of water {x^y) ft. high.
Hence if S be the measure of the specific gravity of
mercury, and h, h' the measures of the heights of the mercu
rial column at surface of the water and at the bottom,
measure of pressure at CD = hs + {x + y)xl.
But measure of pressure at CD^h's \
:. hs + x + y = h's,
.. x={h'h)sy.
Now, by Marriotte's law, if a be the measure of the height
of the bell,
^=^„ or, 2/ = ^,«;
.. x=ih'h)s V a.
!
1
'
•
f
i
:
'
1'
■ fvi
■j,t i
i,
j •
';i
.'k
I' '
90
MISCELLANEOUS EXAMPLES
2. rr//^^ m^<5^ U the least size in cubic feet of an inflated
balloon, that it may rise from the earth when filled with gas
whose specific gravity com2mred with that of air is 08 the
tceight of a cuUcfoot of air being •;} grains, and the collapsed
balloon car and contents weighing altogether 550 lbs. F
T'lking 1 as the measure of the specific gravity of air
^"^ ^ ofthevohimeoftlieiiiflatcdbulh.oM.
wciglit of inflated balloon, )
neglecting weight of envelope, j "^"^^ ^ ^^ "^^ ^^^•
weight of air displaced =(.Fx 1) grs. = Tgrs.
Now 1 cubic ft. of air weighs '3 grs.,
•'• ^ 'SFgrs.;
.'. ascensional force = (3 F 08 F x 3) grs.
= (92x3K)grs.
.'. •92x3r=5r)0x7000,
• • ^= .92 X 3 ^^^ ^ = Q^725 cub. ft. nearly.
3.^ The weight of a globe in air is TV, and in water w ;
find its radius, supposing s and a to be the specific gravities
of water and air.
Let ^ = radius of globe, and P = weight of globe in vacuo.
Then volume of globe = . ttR^ ;
.. P irR'a^ W
P  ttRH = w
o
(1),
(2).
Hence, subtracting (2) from (1),
■^■7TR'{sa)=^lV^W]'
^ (47r s — a j
AflSCELLAJVEOUS EXAMPLES.
«•«•'
an inflated
d with gas
r is 08, t/te
\e collapsed
s.r
>f air,
:edbullfiorj.
gra.
= Fgrs,
4. HoiD deep must a cylindrical diving hell he submerged
fo as to be just half full of water ?
At first tho bell is full of air of ordinary density.
When the bell is half full of water, tho air is compressed
into half its original volume, and therefore the density is
doubled.
But tho additional density is entirely due to tho weight of
a column of water 33 feet high.
Hence when the surface of the water in the bell is 33 feel
Ijelow the upper surface, the bell will be half full of water.
5. A spherical balloon is to he formed of a material oj
trhich the thickness is k, and specific gravity relatively to
air 8 ; if it be filled with gas of specific gramty d, prove that
it> order that it may ascend the extreme radius must exceed
cater w ;
gravitiei
n vacuo.
— V
d)'
I^et ^ = extreme radius.
Then a; « = interior radius.
4
.*. weight of envelope alone  tt [a? {x xf) h ... (1),
o
gas ~ 'jT{x — Kfd
air displaced
(2),
(3).
The balloon will not ascend unless the sum of (1) and (2) be
loss than (3).
.. ^'n{a^{X'Kf}b^\ir{xKfd\TTx''\Q&s than 0;
3 o "
.. a?3 (8  1) less than {x  Kf (8 d\
,\ l*greater thanf g— ,y,
r r
' 'A
f 1* 1
f •
Ih
1
1 . i
' i
' ,■'
'','•
.. 1
i'
'1 .■:
r
ft
92
MISCELLANEOUS EXAMPLES.
.. ^Ie88thaul^3_),
/. a? greater than <
m
6. J^or tico given temperatures the readings of one
tJiermomeler are n^ and m^ and of another v^ and yf
respectively. Wliat will he the reading of the latter when
the former gives ^' ?
(w — in) deg. of the 1st are equivalent to {v — /x) deg. of the 2ivd.
1
1st,
1st
I
2nd.
2nd.
7. A globe, 2 feet in diameter, when boating is half im
mersed in wat^r ; what is its u eight ?
The globe must be half as heavy as water.
4
Now volume of globe = tt cubic feet,
o
and 1 cub. ft. of water weighs 625 lbs.
4 / 47r\
.*. TT cub. ft. of water weigh (6225 x —I lbs. ;
1 / 47r\
.. weight of globe =  ( 62*25 x ^ I l^s.
= 1309 lbs. nearly.
8. A sphere whose radius is 6 inches and wsight ?5 Ih^t
is suspended hy a string. Required the tension of the string/
when the sphere is wholly immersed in water.
4 /l\' TT
Volume of sphere = 0^(0) ^"^ ^*'= « ^^^ ^*'
Weight of water displaced = ( ^ x 62*5^ lb».
/ TT \
,«. tension of string =^ t 35  ^ x 62*5 j lbs.
2'275 lbs. nearly.
MISCELLANEOUS EXAMPLES.
93
75 of one
v^ and fi*
liter when
of tlio 2r«d.
2nd.
2nd.
J half im
nght ?5 Ih^
' the string
9. A pipe 15 feet long, closed at the upper extremity ^ is
placed vertically in a tank (f the name height, and the tank is
filed toilh icatcr. Prove that if the height (f the tcater
barometer be 33/A din., the neater icill rise '3 ft. Oin. in the
tube.
Let a7=nioasuro of height to which the water rijjcs in feot.
Then 15 ;c = measure of space filled with air.
By Marriotto's law, the pressure of the air inside may bo
represented by
15.^• 4
But this pressure is also represented by the measure of a
column of water 33 ^ ft. + a column (15 it) ft.
33 , + 15.t? =
4
l5ic 4'
or
o 255
4
/255Y _ 60G25
V 87 ~ 64 '
x
255
■ 8 ''
225
8
3
.. ;r = 60 ft. or 3  ft.
4
The first result is evidently impossible.
10. If a lighter fluid rest upon a heavier, and their
specific gravities be s and s', and if a body whose sp, gr. is a
rest with V of its volume in the iqyper fluid and V in the
lower, shew that
V : V' = ^a : (xs,
weight of body = weight of fluid displaced,
=sV+s'V\
.. r(o— s) = ^*(«'c;,
i
II
,1^
^
V I
>)
■h
5
94
MISCELLA NEOUa EX A MPLES,
EXAMPLKS. IX.
1. E(iual volumes of gold (s.o. 194) and silver {9^.0,. 10'4)
bahmco 011 a straiglit lever, (1) in vacuo, (2) in water, (3) in
meieury (s.g. 1 ;}•:.). Find tlio ratio of the arms and position
of tlio fulcrum in each case.
2. An inclined piano is immersed in a fluid (s.o. 3) and a
body (s.o. 7) \vei<,diin<^ 7 lbs, in vacuo is supported on the plane
by a horizontal force of 3 lbs. Find the ratio of the iieij^ht and
base of the plane.
3. A balloon filled with Hydrogen (s.o. 07) just rises in
air (s.a. 1). The balloon, exclusive of the Hydrogen, weighs
lOcwt. If a cubic foot of air weigh 13 oz., find the volume of
Hydrogen in the balloon, neglecting the volume of all else.
4. If the balloon in Question (3) rise and rest with its
barometer at threefourths of its original height, how mvich
gas must have been expelled, and how much ballast thrown
out '\
6. Explain why the gas and ballast in Question (4) are
expelled.
6. A cylindrical vessel is made of wood : the exterior
radius is 4 inches and the interior 3 inches, the thickness of
the bottom one inch, and the height of the cylinder 9 inches.
It floats in water when the bottom is 3 inches below the sur
face. Find the specific gravity of the wood and the depth to
which it will sink when a small hole is made in the bottom.
7. A piece of ice, supporting a stone, floats in a vessel of
water. Will any change take place in the level of the v/ater
as the ioe melts ?
^ 8. Shew that in a cylinder immersed as in Question (25)
page 64, the depth of the interior surface below the exterior is
a mean proportional between the height of the water in the
cylinder and that of the water barometer.
9. A cubical watertight box, whose edge is 1 foot, is sunk
to a depth of 80 fathoms in the sea. Find the pressure on the
top.
Would it make any difference in the circumstances of the
box if it were not watertight ?
sr (a. a. 10'4)
ivater, (3) in
mil position
i. 0. n) and a
[)U the pliino
D iiei{^ht and
ust rises in
i;on, weighs
volume of
all else.
)st with its
how much
last thrown
tion (4) arc
10 exterior
hickness of
3r 9 inches.
)W the sur
lio depth to
bottom.
a vessel of
f tho v/ater
lestion (25)
exterior is
ater in the
bot is sunk
isure on tho
nces of the
MISCELLANEOUS EXAMPLES.
95
10. An elastic airti!ht bag has forced into it air sufficient
to fdl If) bags of tho same orignial si/.o. To what depth must
it 1)0 sunk in the water tiiut it may return to its original size,
the height of tho waterbarometer being :5 i feet \
11. A vosssel mado of thin heavy material and containing
7
a cubic foot of fluid, tho specific gravity of which is ^ , floats in
water, tho surfaces of tho water and tho fluid being in the
same horizontal plane. Find tho weight of tho vessel when
empty.
12. In Question (11) if some more fluid of tho same kind
bo poured into tho vessel, will tho surface of the fluid or that
of the water bo tho higher ?
13. A cylinder 30 inches long is composed of lignum vitro
in its lower half and cork in its upper half, and floats vertically
in water. If the specillc gravities of lignum vitje and cork be
11 and 2o respectively, shew that the cylinder will float 2025
inches deep.
14. Two pieces of cork, botli small but tho volume of one
three times that of tho other, aro connected by a thread three
feet long passing round a fixed pulley at the bottom of a tank
of water 2 feet deep. Supposnig the specilic gravity of cork
to be 25, shew that in tho position of equilibrium the smaller
piece will bo totally immersed and tho larger piece half
immersed.
15. Two reservoirs of water at different levels aro separated
by a solid embankment, and a bent iron tube of adequate length
is placed with an end in each. If tho barrel of an airpump
be screwed into an aperture at tho top of tho tube, sheu' that
generally after suHiciently working the airpump th^ water wdl
flow through the tube from the higher reservoir to the lower.
Under what circumstances will this fail to take place ?
16 Two bodies of equd volume aro placed one in each
scalepan of a Ilvdrostatic Balance, and are then innnersed in
two liquids whicii are .uch that the bodies just balance each
other: the liquids aro then interchanged, and it is found that
the bodies balance when one of thorn is just half immersed.
Find how much of the heavier body must be immersed in a
liquid, composed of equal vohimes of tho two liquids, so that it
may just balance tho lighter not immersed.
I
9«
MISCELLANEOUS EX/ MPLES.
11
r
■ is
17. A 8ij)lK)n AliC, cuch braucli of which is less than 30
inches h)ii^', is fille<l ^vith luercury juul botli cuds uro stopped.
It is tli(>n phuetl with tlic end A in a howl ol' mercury antl tiio
end C in a l)o\vl of water, tlio surface of the mercury being
Inicer tlian tliat of the water and liiglier than tlio end C. If
tlio ends ho Riniultaneously unstopped, shew that mercury will
How through tlie tuljc into the water i)rovided that
, bo greater than  ,
z p
z, z' being tho rospcctivo doi)tlis of the end G below the planes
of the surfaces, and p, p' tiio respective densities of mercury
and water.
18. The airvessel of a forcepump is a cylinder of height <?,
whoso section A is tlio same as tliat of tiio piston : the water
lias to bo lifted to height h of tho waterb:irometer above tho
l)ottoni of the airvessel, by means of a pipe of section a and
lioiglit/t : if, when tho pump commences worliiiig, tho water bo
just below tlio valvo in tiio airchamber, find after how many
strokes, each of lengtlh^, of tho piston, tho water will bo at tho
top of tho pipe.
19. A cylinder whose height is 8 inches, is floating with
its axis vertical and its base 6 inches below tho surface of
water : a wciglit of G lbs. when placed on tho top of tho cylin
di.r just brings the upper surface to tho level of tho water.
Find tho weight of tho cylinder.
20. When two metals are mixed in equal volumes thoy
form a compound of si)ecific gravity 9 ; when they aro mixed
in equal weights they form a compound of spccilic gravity 8 ;
find the specific gravities of tlic metals.
,21. A cylindrical jar can just sustain a pressure of 1G5 lbs.
to the sqnai'o inch without breaking, and an airtight piston
which f:ts the jar is thrust down and compresses tho air in the
jar. Find the height of tho jar, supposing it to burst when tho
piston is an inch from the bottom of tlie cylinder, the pressure
of atmospheric air being 15 lbs. to the square hich.
22. In Smcaton's airpump if there be communication with
a condenser through tho upper valve, and tlie capacity of tho
cylinder be half that of either receiver .'ompare the pressures
in tho receivers after two descents aiK ascents of tho piston.
[1 i
NOTES.
97
s than 30
3 stopped,
•y and tlio
;iiry boinj^
ml a If
rcury will
the pianos
I mercury
f height <?,
the water
iibovc tho
/ion a and
) water bo
low many
bo at tho
.ting with
surface of
tlio cylin
,ho water.
inics thoy
wo mixed
uvity 8;
of 105lba.
^ht piston
air in th©
b wlien tho
e pressure
lation with
city of the
pressures
e pistou.
Notes.
1. Law IT., given on page 4, can bo deduced from Law I.,
but the method of reasoning is not adapted to an elementary
treatise.
2. On pago 15 tho construction of tho cylinder and linos
f), 7, 8, 9 are not neccsmrif to tho proof, for it follows at onco
from Art. 34 that
fluid i!'*os8uro at ^ = fluid pressure at D.
3. On pago 2 1 it might bo clearer if wo inserted tho sign
X or the word times between VS, and (unit of weight) in lino
7, also between y and (unit of specific gravity) in lino 14,
and so in several other cases in pages 24 and 25.
4. Tho first sontcnco in page 53 is not quito correct : it
might better stand thus: "The exhaustion of the air is re
tarded by tho difliculty of making tho piston come into close
contact with the valves at A and C, and it nmst always bo
limited by tho weight of tho valve CA"
5 The Aneroid Barometer is so called because no liquid
{^ privative and vr]pi<: "moist") is used in its construction.
A metal cylinder about an inch in height, closed by an elastic
piece of metal, is exhausted, and as the metal covering rises or is
depressed, according to the changes of atmos)heric pressure,
it sets in motion hands like those of a watch connected with
it.
6. In reading the descriptions of the Tumps in pages
67—71 the student must be careful not to derive any erro
neous notions from tho use of tho words S^lcti(rl\^\\^Q. It
is retained (perhaps not wisely) as a technical term, con
venient for distinguishing the lower part of tho pumps from
tho barrel.
7. In tho description of tho Siphon on pago 72 it is said
to be of uniform bore. This is not essential to the worlong
of tho instrument, but it conduces to tho regular action ot it,
and renders the explanation more simple.
y. II.
'I
j 1 . '■
f
u>
98
W"
NOTES.
It IS also stated on page 72 that the longer bnmcn must
be outside the vessel. This is not necessary, for the instru
mcnt will work with the shorter branch outside, provided
that the extremity of that branch be below the surface of
the fluid.
8. To the Thermometers it might be well to add tha*
which is called De Lisle's. This is much used in Russiau
scientific operations. In it the boiling point is marked 0» and
the freezing point 150<>.
9. It should be carefully observed that the freezing point
of a Thermometer is found by plrxing the instrument not in
freezing (catet , but in inelthig ice.
I
1* i
nc/b must
10 instru
provided
urface of
add that
RussiaL
>d 0", and
ANSWERS.
ng point
it not ](n
1. 56f tons.
Examples I. (page 8.)
2. 30 tons. 3. 29G29'62Mb8.
4. 1 oz. 5. 1 oz.
e! The area of a circle whose radms is r is irr^, and tak
ing v' as an approximate value of tt, the answer is 5587 B^wt
Examples II. (page 18.)
1. 20 lbs. 2. 37iVlbs. 3. 7:6. 4. 9:8.
5 10 feet. 6. 12 lbs. 7. 9ib8.
8 Iton 7cwt. 3qr.s. 17 lbs. 9. 11 lbs. 12oz.
10. 22500 lbs. 11. 1125^3 lbs. 12. 2 of its height.
13 Since tho external pressure on the cork increases
with the depth, while the internal pressure is constant, the
cork will be forced in when the former exceeds the latter.
14. 12s tons. 15. IS feet.
1. 165 lbs.
5. 5oz. 6. Iffoz
Examples III. (page 27.)
2. 18:1. 3. 7Voz. 4. 'S.
8. 7776.
•016w
m
9. ri6.
10. 844.
'\ 5
12. cub. in.; cub. in.
1 3. Volumes as 1 : 2, weights as i : 4.
11. 14.
14. 2 : 1.
IK o4 7
16,
17. 9325.
^
•i.
II
N
If
U'
I
%
,
, i
!;
I
t
lOO
ANSWERS.
18. If «fi, c?2, ^3 be the measures of the densities of the
fluids, and d bo the inc;isuro of the density of the mixture
19. 8241... 20. *802... 21. 1841. 22. 161..
23. 313. 24. 8G... oz.
25. The volumes aro as 57 : 1, the weights as 2223 : 97.
Examples IV., (page 42.)
1. 3§ 2. 507870 tons. 3. threefourths.
4. 4dwts. 20i§grs. 5. 4. 6. 3 times weight of tub.
7. twothirds.
8. ^oz.
II. 42 oz.
80
^' 432^"'
12. ^oz. 13. ^^Ibs. 14. 35.
10. 3 oz.
15.
20.
73*
16
19*
24. 12 feet.
16. l
17.
75
91
18. 17f. 19. 2f
21.
1362
2731
22. 2. 23. 47Mbs.
25. 66.
26. Because the specific gravity of salt water is greater
than that of fresh wattr.
23. 1728. 29. 7 lbs. 9jVoz.
30. Edge of cube is 2 feet. 31. r/f}.
height of triangle oo , / ,
""/S ' ' ^^'"cn vertex is
downwards ; 3 : 4 when vertex is u^nvards. 34. 16 lbs.
35. 75. 3G. 2 inches. 37. 9
27. " ' inclies.
b.i
38. I^inch.
30. 4 lbs. 40. 3 lbs. 41. 95 lbs.
42. u^iiL^w) '.w,,{u\w). 43. Increased, if t;.c3
wood be lighter than water. 44. 3 : 2. 4,"). I'l.
141''9
47. Yff^ ^^ '^ nearly. 48. 6^*^ inches.
49. 8i«lbs. 50. 9?i^lbs. 61. 10ft. 62. li
•03. 6 inches. 55. 2?.
.^ 86400 , .
''^ 2053'""^^ "^*
67. rrr, of a cubic yard.
IJfK
es of the
I mixture,
161..
3 : 97.
ANSWERS.
lOI
58.  of volume.
5
59. 750 oz.
85
61. 936302451687 cub. ^^
64. 900 grains.
67. 433 graius.
60. :^ of a cub. ft
w
62. — . 63. m : n.
64. 900 grains. 65. l^J^ or 10272 nearly. 66. '64
• 69. 42^V^cub.m.
Examples V. (page 60.)
lit of tub.
LO. 3 oz.
55.
19. 2f
•s.
5 greater
>jVoz.
ertex is
) lbs.
inch.
, if t;.o
1 :j.
64
times
1. Den8ity = (^^y times original density. .. g^
. . , Q o • 1 4. No . because the
ongmal pressure. 3. J . i. **• , .. ,,,p.„„„t:o,.
pressure varies with the depth alone; so that if ^^^ ^^^
varied there would still be equal vertical increments of space
for equal increments of pressure.
5.
1 J.1
a 11" inches 7. The mercury ^vould fall to the
level of I'i ":^te i„ the cup. 8. U«25 lbs. 9 1« cet
10. No : because a volume of mercury equal to tot
displaced by the irou will desceml ^ ""^ "\'; .t'
its place without disturbing the ^'"'"'''''^^^''^IZ ZlZv
11. Siuk: see answer to (16). . 12 ''"''"'''iioa
would descend a little. 13. 238 square inches. J". 09
. . , 1 1 f; 1 ff^ 'i^^'.^ m 16. vv nen
of oriffiuil volume. !»• i it., o^ ;.,;, f i"
he ifoatiug body is partially i»"7;'> ''".?. ^H,
are d' laced: but the aW««! weight ot floatuig ''O^S ™S' "^
of displaced fluids, which n.ust therefore be constant : there
f„r. when the barometer rises, there must bo a los» water
displacement, i.e. the body rises: «•'»'« ^^ f^Xneces"
utn>osphoric pressure (when the '^'"•<'»'='« .''"^V \ TClv
Ute a'n merited water displacement, and the^lore tl.o body
then sinks a httle. w. i • ^•
22. 26 \i inches. 23. 5 feet.
21. lOSOlbs. ^■^ — 1 . . J
ox c ' \ 25 The air will be compressed mside, and
:o dispiace less waier •. and since it floated originally, it will
now S^^^ . becauso the weight of displaced fluid is nowle.s than
Z weight of the body. 26. 5 times o.nnd pic.sure.
,  . 00 Thf* ^nace between zero
'SI.
;..o.
i02
» I
I •
ANSWERS.
point and any graduation ought to bo loss than the spa^ t
indicated by the number i)hiced against that graduation in
the ratio j^f 17 : 18. 33. 14935 lbs. nearly.
34. yo of an inch. 35. Low. 36. 4t inches.
.( 1
: i
r <
ii
It
Examples VI. (page 75.)
I. It will increase the time of filling the receiver, since
the only effective work would be done by the descending
piston, after passing the hole. It will fill the tank in 3 tinie'^
the original time. 2. 27^ lbs.
3. (a) If the hole be below the level of short end, nv.
effect.
O) If above this level but still in the long branch, all
the fluid in this branch below the hole will descend, and ail
above in the same branch will ascend causing the rcmaindti
of the fluid to flow through the short branch, till the siphon
is emptied.
(y) If in the short branch, all the fluid below the hok'
is this branch Avill descend ; all above in the same branch will
ascend and flow through the long branch, emptying the
siphon.
(5) If at the top of the siphon, the fluid will desceml
in each branch and empty the siphon.
4. 32 ft. 953 in. or 327.9416 feet. 5. The fluid would
descend in each branch and the siphon be emptied.
6. Equally well at both, if the siphon be not too high.
7. No: because the hold is lower than the surface in
harbour.
8. 33 ft. iriin. 9. If the air be removed from the
siphon, the fluids would first ascend in each branch and after
wards flow as usual. 10. The water would rise in the in
verted tube as high as the top of the inserted tube and
afterwards flow out of it. 11. First, the water would soon
cease to flow. Secondly, it would rise in each branch, and
afterwards flow. 12. (a) The water will flow into the
lower vessel. (/3) The water will descend in each branch till
it stands at 34 feet above each surface, (y) The same as \_a).
J 3. Each branch 2 feet.
^l
iNSM^ERS.
103
the spat'j
luiitiun ill
iiii'ly.
'S.
iver, sunt'
escendiii^
in 3 i\m^ir^
t end, (K!
ranch, all
:1, and ail
cmaindti'
le siphon
r the hok'
•anch will
ying tho
I descend
lid would
high,
iirface in
Tom the
nd after
n the in
iUbe and
uld soon
nch, and
into the
anch till
lie as i,u^.
Examples VII. (page 81.)
1 n^ _lio. _80 (2) nf^ ^^ (3) ^^ '^'
r4^ 17 0. ^^ '* (5) 2li; Vl^. (6) ^^^ "^^B;
trs U'. 1120 ((J) 150^ 302°. 3. (1) bO, , 1^5 •
2 m0;'360. (3) ^^ B80.' (4) 320; QO. (5) 5^; 120^
fl _ \lo. _ic)io/ 4. Yes: if the graduations are to be
unifonn.^ ' 5. lo^ Cent, and 51.« Fah. 6. W Cent, and
50°Fah. 7. 400. 8. Make each degree ths that on
Fahrenheit. 8. 25^ 10 20" Cent, GS^ Fah 11. O^".
12 The graduations would be inconveniently small.
?■ 800 Fah 14. 200 Cent, (>S0 Fah. 15. 1 If Cent.,
U^fI 16. 240. 17. 230. 18. 59^oFaim20Reaun..;
if d be the number of degrees, Fah. rises  and Reaum. .
Examples VIII. (page 87.)
1. 4 : 37. 2. 495.
4. 118125 inches. 5. \ : p.
7. Sift. 88 in. 8.
970
10. 80 ''''^•^^'
13. 10 feet.
3. 40° and 6620.
6. 1083.
9. 22ift.
2400
13"'
14. (a) 2 ^ lbs. downwards ;
11. 137F. 12.
0) 2 ^ lbs. upwards.
16. 600 Fahrenheit.
9
18. 15
17'
19,
15. 7 2^5 ^^^ 13 4^^
17. 1220 Fahrenheit.
2. 20. 17 inches from one
end.
Examples IX. (page 94.)
1 n^ 97 • 52 (2) 92 : 47. (3) 59 : 90.
1; (3) fulcrum is at one end, and gold between fulcrum and
silver.
I I
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V.
;•
¥
r'
H
^' ,
fill
ft
li
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104
ANSWERS.
2. 3:4
Q 10x112x16 ^^
120
4. ^ of the gas
1
has been expcllocl, and  of the whole weight thrown out.
5. Gas to preserve equilibrium of internal and external
pressures on the balloon. Ballast to preserve equilbrium of
vertical pressures on the balloon.
6. Sp. gr. = ^ . Height immersed = 5  inches.
7. No change will take place till the stone falls from the
ice, it will then displace less water than before, and the sur
face will consequently sink.
9. Taking a cubic foot of water to weigh 1000 oz., the
resultant pressure is 30000 lbs. The pressure would be the
same inside as outside.
10. 102 fathoms,
surface.
11. 125 oz.
12. The fluid
16. ^.
19. 10 lbs.
22. 33 : a
18.
A (2h + c Jc"" + 4 A^) + a { >Jc^ + Ah^  c)
20. 10 and 8.
2AI
21. 11 inches.
li.i
»iiMiT I I
if the gas
out.
exterjial
ibrium of
from the
the sur
oz., the
L be the
:he fluid
ics.
One of the most popular Text Books ever published.
NEW ELEMENTARY ARITHMETIC
ON THE UNITARY METHOD.
By Thomas Kirkland, M.A., Science Master Normal School,
and William Scott, B.A., Head Master Model School,
Toronto.
Intended as an Introductory TextBooh to Hamhlln Smith's
Arithmetic.
Cloth Extra, 176 Pages. Price 25 Cents.
Highly recommended by the leading Teachers
of Ontario.
Adopted in many of the best Schools of Quebec.
Adopted in a number of the Schools of New
foundland.
Authorized by the Council of Public Instruc
tion, Prince Edward Island.
Authorized by the Council of Pnblio Instruction,
Manitoba.
Withi)i one yehr the 40th thousand has been issued.
ADAM MILLER & Co.,'
Toronto.
\
1 »
i
■
r'
HI
fs.
I
Uighly Commended hy the Press of Canada and
the United States. "
ThG Ith Edition. 50th Tliousaiul iHsuod within nine
niontlis.
Authorized by the Education Department of
Pnnce Edwr.rd Island, introduced in many
of the principal Public Schools of the Pro
vinces of Ontario and Quebec.
elementarTarithmetic
ON THE UNITARY ME HOD.
By Thomas Ktrkland, M.A., Fcionce Master Normal
fecnool, Toronto, and William Scott B A
Head Master Model School, Tor> nto. * '
Cloih Extra. 176 papes. Price 85 cents.
A. B.
WESTEHFELT, H.M.
Mt. Forest.
exc
Model School,
Kirldand & Scott's^Eieinentary Arithmetic is an
icellcnt work. It is intensely practical
SAML. E.
BROWN, Head Teacher, Sep Schools,
Ti London, Ont.
K^ rlum,iTI?Jl??; oxaniiued your Elementary, (by
Ivnklnnd & bcott) and I consider it far superior to
any other book of the kind with wliich I am ac°
quainted and just what we require for onrTnior
classes. I will introduce it immediately. ''
ST, MAEY'.S ARGUS.
The arrangement of the work is thoroughly ration
al, the oral and slate exorcises are exactly what is
needed, being sumci.ntly simple and yet wl 1 cal
culated to develop tlie thinking faculties while the
wovVhr„n the simple and Uniform system of
m ,1 pi^thl F^'^V^^""^ '^y analysis and deduction
n) +1.1 ^ book correspond with the method
of teaching arithmetic now beinc adontpd
by all iutelUgent teachers. ^ aaopted
EDUCATIONAL JOURNAL OF VIRGINIA
This volume presents in a condensed form" all
that is needed in an elementary book.
Th^^S'^^^T^^^^'.^^^'^^^^ Granby Academy.
qpott S !i^?''H'"^i Arithmetic, by Kirkland and
Scott, IS estimated so highly by me, that I shall
At:^^u.T^}''^^ ^\''^% ^° '^^^^'^ '* introduced into the
t ly A\ oik, there is no textbook in use which
equals .It in all that is necessarv both fr™the
standpoint of the teacher and pupil.
KIRKLAND AND SCOTT'S ELEM. ARITHMETIC.
SCHOOii BULLETIN, Syracuse, N. Y. >
Wo thiuk tlio book is oue of decided merit.
A.
KENNEDY, Head Master Martintown Model
School.
I consider it the best contribution to arithmetic
which hiiH boon marie of lato years. The arrange
ment of tho work in oxcollont, the exorcises being
well adapted for boj^inners, each series preparing
the pupil for the next.
GEO. B. WAED, M.A,, Head Master H. S., Orillia.
I have used the work with private pupils pre
paring lor the entrance examination, and have
derived much satisfaction from the plan ol
the subjects and the exphiuations therein.
The method of reasonina adopted afforded
creat pleasure to the pupils also, who tiius seemed
to be able to dispense with much oral instrction.
The miscellaneous examples and tho hints fo. ivork
in" some of thom are very valuable. I speak ol
wapils drspensing with oral instruction, not that
this is advisable, but merely to 8^.>.ow that the
methods are so clear that alter following the ex
planations tlie pupils were easily enabled to work
out mentally any given example.
A. C. OSBORNE, H. M. Model School, Napanee.
I do not hesitate to pronounce it, as far as I am
capable of judging, a vast improvement on the text
books heretofore used. Considerable prominence
(though not too much) has rightly been given to the
''Unitarv Method" nnd tho method of enunciating
principles by example and deduci g the rule there
from, backing them up by the vast ">J"'^e,^' «* l^^l'^^'
tical nroblems, materially enhances the value of the
work I ifke very much the style of introducmg
practical problems from the beginning.
A.D. McQUAKBIB, Hearlmaster Valleyfleld Model
School, Quebec,
The Elementary Arithmetic is just what is re
quired, and I believe will be, in the liand of an
experienced teacher, far superior to anything A\e
Jiave had.
The Daily Expositor, Brantford, Ont.
Kirkland and Scott's Elementary Arithmetic is a
biglaly practical little bock, intended as an intro
ductory textbook to Hamblin f^mith's Arithmetic.
The authors are well known for their l^g^Y.Sf h^
in scholastic circles and practical knowledge ot the
teaching profession^
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KIRKLAND AND SCOTT S ELEII. AIUTILMETIO.
A. C. A. DOANE, InRp.,Rholl.urnn Co., No» a Scotia.
I am much ploiiHoil with tho Kloiuoiit iry Arith
metic l)y Kirkland iV: Scott, it is oiio of tlib host of
tlu) liiml I have Hoon. Tlio (ItiHiiitioiis ami oxphina
tioiiH arc fiimiilo and may bo ousily untl(»r8to(i(l, tlie
mental oxorcisos and problems aio calcuiatod to do
velop thouf^ht and hIiow tho practical nHcH of tho
scionco, tho roviowB toad to ])iodnco th'ivdUi^hiicHfl,
and tlio examination papcrH Ktsrvo t,o test tho pupil's
capacities and tho oxtunt of their iic(piisiti()n9. On
the whole it isadmini.blyadaijteil to tlio elementary
departments of our common schools, and as such
deserves to come into general use.
A. ANDREWS, Hoad Masu: NiiiRara H. fl.
Tho Elementary Arithmetic will seiw. ..., .u capital
introduction to tho Canadian Eiiitiou of Hnmblin
Smith's Arithmetic. These two, aloii'^ with lOxami
nation Papers by McliOilan ife Kirkland, and tho
Mental Arithmetic by Dr. IVIcLollaii, hxivo touchers
notiiiiiR more to dosiro in tho way of textbooks on
this subject.
Tho Dumfries llrfomier, Ont.
The avrangemcnt of tho work is thoroughly
rational, and the ornl and hlato exorcises uvo < xiict
ly what is needed, beiiij,' sullirientlv simple and yet
well calculated to ilevelep the thiiikiiif^ fucultioa,
while the adoi)tion of liie simple and nnif.rm sys
tem of working all proldems by analysis and deduc
tion makes tho bc.jk correspond with the method of
teaching arithmetic now being ail()i)ted bv all intel
ligent teachers. This mo,st excellent littlo book
det:erves general introducLion to the junior depart
ments of our common schools.
J. F. JEPFERS, M.A., H. M. Coll. Inst., Petnvboro^
. The Elementary Arithmetic bv Messrs. Kirkland
& Scott is valuable for its simplicity of definition,
omission of things obsolete, and for the rational,
practical nature of its examples.
T. L. MICHELL, B.A., H. M. High School, Perth.
I have made a careful examination of the Elemen
tary Arithmetic by Kirkland & Scott, and have no
hesitation in attesting to its merits as a text l)o<)k,
both in rospect to matter and tlie luaniier in which
the different steps are introduced. It is a good juo
paratoiy boolc to Haniblin Smitii's Advanced AriMi
metic. and as such siiould be introduced into every
public school in the land.
E. ALEXANDER, H. M. G.alfc Model School.
I am plaased with the arrangement of tlis subjecta
and the practical character of tho problems. It iij
very suitable for junior classes.
HAMBLIN SMITH'S
MATHEMATICAL WOPtKS
AU USBD ALMOST KXCLUSIVCLT
In the Normal and Model Schools, Toronto;
Upper Canada College; Hamilton and
Brantford Collegiate Institutes; Bow
manville, Berlin, Belleville, and a large
number of leading High Schools in the
Province.
HAMBLIN SMITH'S ALGEBRA,
With Appendix, by Alfred Baker, B.A., Mathematical Tutor, Uni
versity Colloye, Toronto. Price, 90 conta
THOMAS KIRKLAND, M.A., Scir o Master, Normal School.
"It is the texthook on AlgcV :i for candidates for secondclass
certificates, and for the Intormc .co Kxamination. Not the least
valuable part of it is the Appeuc' by Mr. Baker."
GEO. DICKSON, B.A., Hea jlastcr, Collegiate Institute, Hamilton
" Arrangement of subjects good ; explanations and proofs exhaus
tive, concise and clear ; examples, for the most part from University
and College Examination Papers, are numerous, easy and progres
sive. There is no better Algebra in uso in our High Schools and
Collegiate Institutes."
WM. R. RIDDELL, B.A.,"B. So., Mathematical Master, Normal
School, Ottawa.
" The Algebra Is admirable, and well odapteJ as a general text
book."
W. E. TILLEY, E.A., Mathematical Master, Bo\vman^•ille High School.
" I look on the Algebra as decidedly the best Elementary Work ou
the subject we have. The examples are excellent and well arranged.
The explanations are easily understood."
R. DAWSON, B.A., T.C.D., Head Master, Hish School, Belleville.
" With Mr. Baker's admirable A)pendi\, there would seem to be
nothing left to be desired. We have now a firstclass book, well
adapted in all respects to the wants of pupils of all gmdes, from the
beginner in our Public Schools to the mo.st advanced student in our
CoUcnate Institutes and Uvxh Schools. Its publication is a great lx)on
to the overworked matbomatical teai^hers of the Province."
I I I
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Km 1 1 _
ft.
HAMBLIN SOUTHS ALGEBRA.
VViih Apncn.lix by ALFKKD UAKEH, D.A., Matheinaticiil Tutor,
University C'lHejje, Toronto. 4th li^tl., go cts.
Anthcrized by ttie Minister of Education for Onturio,
Authorized <;;/ the I'.uuucil of Puhlir Iiintrnitioii for Quebec,
Hecammended by the Semite of the Univeraity of' Halifax.
o
0. MACDONALD, Prof. MathemiitlcB, DallioviBlo College, Halifax
" I have received a Bot of your Mathotiiatlciil I'lihlicatloiifi, viz.,
the TroiitlHOR on Arithniotic, Alt,'obra, luid (iooiintry, by Mr. Hiuiib
liu Sinitli. Tiioy all Booiu to 1110 adiuirablo troiitis'es, and fUtod to
be the text bf)()liH for inoro thoiou^jh atid RoloiitiCic touc'iiiif! tliun
hu8 yot found Its way into the majority of our lu'^li hi^IiooIh and
aciidoiiiiort. Of tlio coiiiouB oxoroiHoa in (iloinotitnry al^jchrnio, i)ro
cesHt'H every tlioroii,'!! toaclior will a))i)it)vo, Kinco oxixnioiico sluiwa
tliat, as dlHcipliiio in >,'raininar is the main roMiiirouKsnt of tlie
yountjBtiidont of claHsicH, bo praotlco in aUtobrnic ninniinilatioua is
the finidaiuontal ro<iiiiioniHnt of the nJii'bi.iiHt. 'l'}ion a^jain, tlie
refoionco of oqnatioiiH involving the trcatnjcuit of radicalH to a
■oparato and advanced Bootion, inarlvM t .0 antlior as one who lias
■lytiipatliy with the dillicnltioa of bogititierH. The oxposlMoiiR are
uniformly fiucclnct and clear. Tijr i;..'onu!trv has moiits fninally
hlRh. Manjy of Kuclid's mothoda ait iuiiirovod on, ami propositions,
not as in hiiclid, dednccil from a common principU). 1 may instance
two proposit ions In the 3rd book,thn2'2nd, and the :ilst. Tlio iiiuthod
of Btiperpositiou of trianfiles emphvod in tlio earli(n proposiLionH
of the Olh book, will b'j to many a strikinj;? novelty, and it i.s uniform
Of conrHe, many of us, from long practice In expoundiii!,' and iiritj
cising Euclid's olomout, had arrived long ago at these mctiiodi'
Hut it may be doubted if they are generally known Tiicv ai „
mupiostioiinbly preferable to the old, though Euclid's mftltodn
ought to bo explained along with them. We want sadlv a, nationa,
Euclid, and this is the best iipproximation to it thjit i have Komi.
We in DalhouHio include these books as admissible and rcciom
mended text books iu our nuithematical classes of tho first year.
They are sure to come iuto extensive demand, as thoir merits come
to be recoynised.
B,
C. WELDON, M.A., Math. Master Mount Allison Collece.
Sackville, N. B.
Wo are using your Algebra in our Aca«omy.''
A. 0. A. DOANE, Inspector of Schools, Barrlngton, N. S.
"The algebra as an elementary work contains all that is nooded
for our better clasr, of common schools. The armngoment is such
an to lead the studont from tirst ])riuciplc8 gradually to tho intri
cacies of the Bcit'iice, and then with lucid discusHions to unravel
those intncacies and bring the whole under the comprohonsion of
every ordinary intellect. The exaiuinatiou papers form a valuable
and useful part of the work. I can unhesitatingly recommend it
to teachers us > .11 adai ted to aid them materially in thoir work,
and to Btudents r, a te>t book weU suited to their needs.
0. T, ANl>I<Jii\v'S, Inspector for Queen's Co., N. S.
"I have examined Hamblin Smith's algebra and found the ex
amples admirably arranged in a progressive order, easy and Avell
adapted for the use of our public schools, into which I Bhall be
pleased to recommend its introduction.
HERBERT 0. CREED, M.A., Math. Master Normal Scotia,
I'Tedericton, Is.B.
"I have made sufTicient acquaiutance with Hamblin Smith's
algebra to be satisfied of its excellence as a text book, and to war
rant me iu recommending it to one of my claues.
i
aticAl Tutor,
frfo.
>r Quebec.
1 1 ill fax.
lloge, Halifax.
licatloiifi, viz.,
by Mr. Miutib
, a!ul fUtoil to
Loiic'iiiif; tlian
li H(iho(ilH anil
ilfjfhiiiic, j)ro
orioufo k1u»W8
oiiitiiit of the
tiipulatiouH is
ion nt,'iiin, tlie
rtiilicalH to a
H Olio who iias
cpositioiiR aro
lorits P(iiinlly
1 propositions,
may instance
i. Tlu! iiiuthod
!■ propowitiona
1 it is uniform
liii;,' aiKl critj.
icHO nictliotlg_
n. Thoy ai ^
id's llW't'ltOllg
lly a, national
t i havo Konn.
and THcioni
tho lii'Ht year.
r moritscoino
on College,
on, N. S.
;}iat is nooded
ouient is such
y to the iiitri
)nrf to unravel
prolicnsion of
Lni a valuable
rocomniend it
in thoir work,
ids.
N. S.
fonnd the ex
oasy and avcII
cli I Bball be
lol Scotia,
nblin Smith's
k, and to war
THREE EDITIOiNS SOLD IN SIK MONTHS
OP—
HAMBLIN SMITH'S ARITHMETIC,
ADAPTED TO CANADIAN CUKRBMCT
THOMAS KIRKLAND, M.A., Sclenoe xvTaBter Normal
School, Toronto, and
WM. SCOTT, M.A., Head Maater Model School, Ontario.
4th Edition, Price,
76 Centa.
AutluyHzed by the Minister af Edueatinn, Ontario.
Authorized by Ihe Council of Public Inatructiou, Queb4e,
Recommended by the hknato of the Univ. of Halifax.
Authorized by the Chief Supt. Education, Manitoba.
FROM NOVA SCOTIA.
A. 0. A. DOANE, Inspector of Schools, Barrington, N. 8.
" Eamblin Smith's arithmetic seems very suitable to the necei
sitlea of our public schools. The exorcisos arc i^^l''''"' •'!«• '''"Ji*^^
examination papers are invaluable as aids to tcunhers m thorough
tfaininff Thoy will also prove of groat son'ice to pupi s desirous ■
of passing the grade tests. The author appears not to volv so much
Sn set nUes al upon explanations and tho clearing of seeming
Sbs?urit 08, 80 that pupils may readily comprehend the questions
and proceed to the silutions. I cordially recommend its use to all
those desirous of obtaining an acquaintance with this branch of
aseful knowledge.
0. F. ANDREWS, Inspector for Queen's Co., Nora Scotia.
" I have much pleasure in certifying to the superiority of the
Canadian edition olf HambUu Smith's Arithmetic over any text
book on that subject that has yet come under my notice. It is
practical, complete and comprohensive The appendix 'fd exam
ination papers are important and valuable^^features. I shaU be
pleased to recommend its early introduction.
W. S. DANAGH, M.A., Inspector of Schools, Cumberland, N. S.
HAMBT.IN Smith B Arithmetic.— "It has a value for candidates
preparing for public examination, as the examples have been
mostly culled from Examination papers, indeed I may say that I
have not seen any other workontliia branch that is «o socially
calculated to assist the student in passing ^jth credit oi^ctaJi«at«.
I therefore think that HambUn Smith's Arithmetic should be
ploced on the autJiarized list of books for public schools.
! f' J!
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EXAMINATION PAPERS
m
ARITHMETIC,
s
^^m' A.. MoLellan, LL.D., Inspector High Schools, and >
Thos. Kirkland, M.A., Science Master, Normal School. 
Toi onto. ■§
e
PRICE $1.00. ^
e
 '— « g
e
Prom the GUELPH MERCURY.
fT «; * ,V !P^^, ^°^^ *^ divided into six chapters. The iirst is on the
Unitary Method, anri given solutions showing, its applicvatlon to !
variety of problems, in Simple and Compound Proportion Percentage
Interest Discount Profit and Loss ; Proportiona' Parts/l4r neSv
S'nT ^"'«' „J?^«'?,^»ye, Alligation; Commission, 1. sura, ee ScT.'
fetoclis and Miscellaneous Problems. The second is on Elenientarv
Rules, Measures and Multiples, Vulgar and Decimal Fractions The
third contains Examination Papers for entrance into High Schools and
Collegiate Institutes, the fourth fur candidates for thirdclass ccrtii
cates, the fifth for candidates for the Intermediate Exam nation ad
secondclass certificates, and the sixth for candidates for th rdclass
certificates and U.nvtrsity Honours. It vill be observed that the wrk
begins with the fundamental rulesthoss principles to be acnui rod
when a pu,)il first enters upon the study of Arithmetic, and 2nries
^InZrii^'V'^^'^'?"^ *"^ ^^^ highest class of certificates and S
Honours of the University. . . . Teachers will find in it a necessarv
help in supplying questions to give their classes. Those who asiSe S
5L*!f;''^\T ^^V'^'^'l ^''^^^ ''^^'"^'• guideindeed ^here is not soSd a
one— on the subject with which it is occupied.
From the ADVERTISER.
*y, ' u ' ?y *" ''^° *'"® ff^'^PJ"? after some method better tlian
they have at present, this volume will bo cordially welcomed aSd
many who have never suspected the possibility of accon.S Sir so
much by independent methods, will be, by a perusal of en troduc
tory chap er impelled to think for themselves, and enabled to teach
their pupils how to do so, . . . It is far buperior to amthin of the
kind ever introduced into this country. . . . The tv> o"rin v. n
aj.pearance of the work is of a very higii diaracterqiXtou'' i'
arnSe^lI'^^ '''' '"'^'^ '' ^^^ ^' publish Sui ^'i
d
<p
a
a
o
o
a
o
• rH
Sl
a>
a
<!
a
o
m
a
i— t
■o
o
From the TELESCOPE.
. . . The plan of the work is excellent, the exercises heine
arranged progressively, each series preparing the student for the next
The problems are all original, and so constructed as to prevent the
student using any purely mechanical methods of solution We
should really feel proud of our Canadian Authors and publ'ishin
houses, when we consicler the infancy of our country and the progress
it has made and is raaking in educational matters, and particularry it)
the recently published education^ works. "wuuuij mj
RS
s
1I3, and g
liool, ^
e
PSA
g
3 on the I
n to a =.
centage, "g
iiersliip; qj
Je, &c.,.S
rnentary '^
s. The o
)oIs and ^
ccrtili rt
ion and
irdclass
lie work
.cquircd
carries
and for
'cessary
spire to
) good a ra
a
o
• rH
(1
a
<!
a
o
o
;r than
^d, and
ling so
troduc
teach
; of the
ai)hical
[ual, ui
uses ol
s being
e next.
mt the
. We
)lishin:j;
•rogrcss
lorly iu
DR. MCLELLAN's mental ARITHMETIC.
From the CHATHARi PLANET.
This book will prove an important auxiliary In the
study of arithmetic.
A. C. HEREICK, Head Master of Public Schools,
Coilingwood.
McLellan's Mental Arithmetic, Part I., is every
thing tliat can be desirod as such. It should be in
the hands of all teachers. Its Fource is a sufBcient
guarantee for its thoroughness. I would be pleased
to see it introduced into all our schools.
R. KINNEY, M. D., Insp. Public Schools, District
No. '2, Leeds.
Well adapted for use in our public schools.
D. H. HUNTER, M.A., H. M., H. S. Waterdown.
It is an excellent little work, which will supply a
want lonp; felt by Canadian teachers.
J, FRITH JEFFERS, M.A.. Coll. Inst., Peterborough.
The Mental Arithmetic by Dr. McLellan supplies
a want in our list of textbooks. Ever since the
introduction of the unitary method of teaching
written arithmetic there has been needed such a
guide in mental exercise. The methods of opera
tion and the character of the examples make the little
book worthy of a prominent place in school work.
W. H. LAW, B.A., Prin. High School, Brockvilla.
It will supply a very great defect, and I am
sure the profession will cordially welcome it.
Rapidity with accuracv is not found in our schools,
and the'Do' tor's excellent publication will admir
ably accompiish these results.
J. H, McFAUL, H. M. aiodel School, Lindsay.
It is a most excellent drill manual, and should be
in the hands of every scholar.
A. BOWMAN, M.A.,H.M. High School, Farmersville
The Mental Arithmetic, like its author, needs no
commendation. It was needed, and will bo much
nsed.
M. MCPHERSON, M.A., IT. S. S., Prescott.
You certainly deserve the thanks of all who aie
interested in the education of our youth, for your
efforts to sup)ily our teaohors and pupils with suit
able text boMiS. I iim pleased with McLellan s Men
tal Arithmetic, and hopo it will soon be m the hands
of every teacher in this Province. Were mere atten
tion Given to m.'Tital arithmetic in the tinmary
classes m our Public Scnools, there would be fewer
failures at our second class and intermediate exa
minations.
i I
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f: •[
i! ' :
ENGLISH GEAMMAK
BY C. P. MASON, B.A., F.C.P.,
Fellow of University College, London,
With Examination Papers by W. Houston, M.A.
PRICE 75 CENTS.
ALEX. SIM. MA., H. M., H. S., Oakville
. Upwanls of three years ago I asked a giammar school nepectot
m the old country toHeud ino the best grammar ijubli he<? there.
He immediately sent me Mason.
A. P. KNIGHT, M.A., H.M., Kingston Collegiate Institute.
Incomparably the best text book for the senior classes of our
high schools that has yet been offered to the Canadian public.
J. KING. M.A., L.L.D., Principal. Caledonia, H. S.
Mason's giamraar will be found a niost valuable classbook ^b
pecially for the mstiuction of advanced classes in EngUsh The
chapter on the Analysis of difficult smtcncos is of itself bufflcient
to place the work far beyond any EngUsh grammar hitherto be
fore the Canadian public.
RICHARD LE\VTS, H. M., Dufferin School Toronto.
As a philosophical treatise its discussion of doubtful points and
Its excellent methods and definitions cannot fail to rive it a hi^h
rank m tile estimation of the best judges of such works— the scho^ol
teachers of the country. It has reached a twontvllrst edition iu
England and I have no doubt it win meet witli the same high ap.
preciation m tins Pro%lnce.
JOHN SHAW, H. I\r., H. S., Omemee.
, '^* *^^'fso^'8Grarauiar is just such a book as many teachers
nave been hoping to see introduced into our sobools, its method
being to teach the subject by explanation, dcliuition and abun
dant illustrations without stereotyped rules thereby makiut' the
study even attractive.
D. C.MacHENRY, B. a., H.M., Coboiug Col. Institute.
It is an excellent and reliable work. It will be well received by
teachers and advanced pupils.
JOHN JOHNSTON, P. S. I.l^lleville and. South Hastings.
Of all the grammars that I have seen, I consider Mason's the
best. ^;. 0»
•^~ L % ^
J. MORRISON, M.A., M.D., Head Master, High School, .Newmarket.
I have ordered it to be used in tliis school. I aonsider it by far
the beat English grammar for high school i)mn)osos that has yet
appeared. With "Mjuion" and "liemiug" nothing more seema
to be detired
TO AVOID CONFUSION, ASK FOB
IIILLBU'S SWINTOIT'S LANGUAaS LESSOITS,
The Blew Aiuaiorizccl Graanniar,
fi!ILLEfi'S SWINTON'S LMGOIIGE LESSOiS,
BY J. A. McMillan, b. a.
The only Edition prepared as an Introductory Text Book to
MasoWs GranimLur.
In Miller's Edition of Language Lessons Tlie Dennitions of
file Parts of ?»pcecli are noiv luadc ijJeiitical ^vitn
Mason's GiaKaaiar.
The Classiflcatlon of Pronouns. Verb", floods, and
Cieneral 'I'realiueut are the same as iu Mason's TCXt
Book.
Miller's Kdltlon is prepared as an introductory Text Book
for Mason's txrammar, the authorized hook for advanced clat^ses
for Puhlic Schools, so that what is learned by a pupil m an cl.'mcn
tary textbook will not have to he unlearned when the advanced book
is used, a serious fault with many of the graded Public School Books.
Miller's llldition contains all the recent examination Papers
set for admission to High Schools.
MIIiliER'S SlVIIV'rON'S LA>'«UAGI': LESSONS
is authorized by the Educatiou JJepartinent of *. mtario,
is adopted by the SchooLs of Monire d,
is authorized by the Council of Public Instruction, Manitoba.
To the President and Members of the County of Elgin Teachers
Association: ,,,,,, , \ e
In accordance with a motion passed at the last regular meeting ot
the Association, appoincing the undersigned a Comiuittoe to con
sider the respective merits of difterent Enghs.. Grammars, witli a
view to sug;>est the most suitable one for I'ublic Schools, we beg
leave to report, that, alter fully comparing the various editions that
have been recommended, we believe that " Miller's Swinton's
Language Lessons" is best adapted to tlie wants of junior puyuls
and ''would urge its authorization on the Government, and its unro
duction into our i'ublic Schools.
St, Thomas, Nov. 3uth, 1878.
A. E. Bin LEII, Co. Inspector.
J. McLEAN, I own Inspector.
J MILLER, M.A., Head Master Pt Thomas Hich School.
A. STEELK, B A., •• A>liner High School
N. M. CAMPiJELL,
Co. of Kigiu IModel h^ehool.
It was moved and seconded that the report bo received
adopted —Carried unanimously.
d
Price, Olotli Exti'a,
*">
ADAM MILLED & CO.
rf!)
Whole {Series in one Voiume Uomplete, $1.00.
• i
f
n
n
:a
H:.R
The New Authorized Eleinentnry (irram in nr.
MILLEri'S SWIHTON'S LAHSUACE LESSOHS.
M[f>i.f:r's Swinton's Language Lessons is used exclu
sively in nearly all the Principal Public and Model
Schools of Ontario. Among them are
4M(ana, HaiiiiKoii, >Vliitii^, I'oitUope, C'oboiirg, Alitclicll.
A.. •aji'>e,
SiraiUroy,
^indtor,
Scaforiii,
liniokville,
JMcai'oi'd*
tliiitou«
Listowcl,
St. i'nlharincs,
Itrantl'ord,
Fertli,
Belleville.
LiiKlsny,
Uxbrldge.
St. Tiionias,
Braccl>rids<'«
A(loi>(ed bj the Fiotestant Schools of IHoatnal and Levi
lolleso* Quebec, Mchools of IViiieiipc^, Itlanitoba,
and St. Jiihu's, ^e^y Foundlathd
Resolution passed unanimously by the Teachers' As
sociation, (North Huron), held at Brussels, May 17, 1878
" Kesolved, That the Teachers at tliis Convention are of
opinion that 'Miller's 8\vinton Language Lessons,'
by McMillan, is the best introductory work on Grammar
for l^ublic School use, since the detinitions, chissitication
and general treatment are extremely simple and satis
factory."
In my opinion the best introductory Textbook to
Mason's Grammar. All ]3upils who intend to enter a
Hiidi School or to become students for Teachers' Certiti
cates, would save time by using it.
W. J. CAPtSON, H. M.,
Model School, London.
The definition's in "Miller's Svvinton Language Les
sons" are brief, clear and exact, and leave little to be
unlearned in after years. The arrangement of the sub
jects is logical and jDrogressive, and the book admirably
helps the judicious teacher in making correct thinkers
and ready readers and writers
L. W. WOOD,
1st A Provincial H., F.S., Trenton Falls.
Be carelnl to asU ?oi' H:ii!.s:K?s s^f 8M'0.\, as o:ii retiUi;;ns
ill «■ in liic ittarkti.
iiniiir.
LESSONS.
used exclu
and Model
!'S, Mitchell.
€nlharinos«
intrord,
lla,
llcville.
il and Levi
Diloba,
eachers' As
ay 17, 1878
ntion are of
a Lessons/
in Grammar
lassitication
e and satis
sxtbook to
to enter a
lers' Certiti
:. M.,
, London.
muasre Les
little to be
of the sub
c admirably
ct thinkers
iiion Falls.
i'
J
* In n.aking history attractive to the
young the Author has proved his apti
tude in a di'piirtiucnt of literature in
which f.'w distinguish tliemselvcs
The uarativo is so sustained tliat those
who take it up will have a desire to
read it to the end.'
Dundee Advertisek.
THB EPOCH PRIMER
Of ElVOLISn HISTORY.
Being an Introductory Volume to the series of Epochs of English IJistoryt
by the Eev. MANDELLCllEIGHT(.)N, M. A., late Fellow and Tutor of Mer"
ton College, Oxford; Editor of Epochs of English History.' Ecp.8vo.pp
148, price 30 cts. cloth.
'As all the leading features— political,
social and popular— arc given with
much impartiality, it can hardly fail
to become a school classbook of great
utility.' Wor.CEHTER JotTRNAL.
' The Rev. MANDKLijCKEiuirio:; has
really succeeded in making an admir
able resume of the wliole of tlie prin
ciple events in English history, from
the time of the Koman Invasion down
to the passing of the Irish Land Act
in 1870. Interesting, intelligible and
clear, it will prove of great value in
tlie elementary schools of the kingdom;
and those advanced in years might find
it very handy and useful for casual
reference.' Northampton Herald.
' This volume, taken with the eight
small volumes containing the accotnita
of the diifereut epochs, presents what
maybe regarded as the most thorough
course of elementary English History
ever published Well suited for
middle class schools, this scries may
also bo studied with advantage by
senior students, who will find, instead
of the mass of apparently unconnected
facts which is too often presented in
such works, a careful tracingout of
the real current of history, and an in
telligible account of the progress of the
nation and its institutions.'
Abkudekn JOURNAIi.
' The whole series may be safely
commended to the notice of parents
and teachers anxious to find a suitable
work on English history for their
' Tills volume is intended tobe in
troductory to the Epochs of English
History, and nothhig co.d be better
adapted for tiiat purpose. The little
boolc is admirably done in all respects,
and ought to have the effect of sending
pupils to other and full( r sources of
liistorieal knowledge.' Scotsman.
'Mr Chi iohton'^ introduction to the
Epochs of English History covers in
a hundred and forty pages more than
1800 years, but having regard to its
extreme condensation is well worthy
of notice. On the whole the work is
admirably done, and it will no doubt
obtain a very considerable sale.'
ATIIENiEUM.
*An admirable little book that can
scarcely fail icr obtain a considerable
popularity,! notwithstanding the great
number of previous attempts made to
relate the history of England in a very
small compass — In this epitome the
epochs become chapters, but an in
teresting account is given of such
events as are likely to be attractive, or
even moderately intelligible to young
readers.' VVelsiiman.
' The excellent series of little books
published under the title of Epochs of
English History, edited by the Rev.
MANDEiiii Creighton, M. A., and writ
ten by various able and eminent writers
being now complete, the Editor has
prepared an introductory volume, cal
led t>.o Epoch Primer, comprising a
concise summary of the whole series.
The special value of this historical out
line is that ii gives the reader a com
prehensive view of the couiso of mem
orable events and epochs and enables
hira to see how they have each con
tributed to make tlio British Nation
wliatit is at the present day.
Literary Woeld.
children, inasmuch as the several
volumes are simply and intelligibly
written,without being overloaded with
details, and care has been taken to
bring every subject treated on within
the comprehension of the young. The
nambypamby element, which is so
often conspiv;uous in histories for
children is' entirely absent, and the
works in question are certainly amongst
the best of the kind yet issued. The
little volume now under notice, which
brings the series to a close, is fully
equal in every respect to the preceding
ones, and it will be found exceedingly
useful to every one who may have to
teach English history.' ^r^
Leamington Coubier. '
^s
ll
••Epochs in History mark an ^^^cn in the Study of it."
^ G. W. JouNSON, H.M.M.S., >£aimlton.
An Acceptable TextBook on English History
AT LAST FOUND I
EPOCHS OF imim history,
BT
REV. M. CREIGHTON, M.A.
Autlioriz<od by tlie Education Bepartment.
Adopkd by the Public ScJwols of Montreal, and a number of
the best Schools in Ontario.
" Characterized by Brevity and Comprehensiveness."—
Canada Presbyterian.
" Amongst manuals in English History the Epoch
Series is sure to take high rank."— Daily Globe.
*' Nothing was more needed than your excellent
Primers of English History."— Fked.\V.Kelly,M.A.,B.D.,
Lect. in English History, Eligh School, Mont eal.
In Eight Vohmes, 20 cents each,
—on—
WHO LE SEHIES in two VOLS. ONL Y 50c. each.
Part E Contain First Four of the Series.
Part IE Contains Last Four of the Series. 
^DAM MILLER «& CO.
TOEONTO.
t."
iamilton.
itory
ORY,
[.A.
lent.
umber of
:ness." —
e Epoch
excellent
.A..B.D..
lONTO.
CHEI&HTON'S EPOCHS OF ENGLISH HISTORY
■o
Ecv. Geo. Bi.aik, M,A,, I. P. S., Grcnvillo County.
"This little work, published in tight miniature voUunos, at 2(Uj.
each, is p( culiarly aduptid for u^^e in our Public and llifth Schooli.
Proaentfd in tbis simple and attractive I'orni, each of the great
epochs of I'lnglish History can ho cheaply, easily, and thorouglily
mastered before proceeding to the next."
Thos. Carscadden, B.A., Head ]\lastei'. High School, Richmond
Hill.
"I can most cordially recommend thom to all students who are
candidates for the Intermediate, or teachers' examinations."
J. TuBNBVLii, B A., Principal Jligh School, Clinton.
"I have examined the 'l':pochs of tiigl'sh History' and have
formed a very higli opinion of them, so much so, that 1 intend to
introduce tliem into the liigli Scliool here. A a to the si /.c and ex
pense they have hit the happy mean, containing all that is really
necessary and nothing more."
H. J. Gibson, B.A., Head Master, Renfrew, H. School.
•• I have ciuefully examined your 'Epochs of History,' and be
lieve them to be admirably adapted for preparing teachers for certi
ficates. They are very neatly got up."
John E. Beyant, B.A., Clinton.
"I have been anxiously waiting for a Canadian edition of these
delightful little books, and now that we have these, I shall introduce
them into my classes as soon as possible."
A. Ding WALE Forutce, P. S. I., Fergus.
" I think it is a great mistake, at a time when imagination is pe
culiarly vivid, to expect history to be studied from the hare hones
laid down, and that the little work referred to has been prepared in
a simple, interesting way lor tliose eomniencing the study of history,
and fitted to carry them on by the grasp th< y can take of the subject
as it is presented, and as one event is connected with another, I
think some such introductory work was much needed."
J. M. Plati. M.D., P. S. I., Picton.
'•Neatness of 'get up;' sin)plicity of langiuigo ; faithfulness of
record; perfection in arrangement; interest of narrative ; concise
ness and freedom from dryness ; or recital of facts, are but a few of
the recommendations of these beautiful little works."
P. H. Michel, B.A., H. M., H. S., Perth.
"It has been said that a book that would sui)ply the place of
'Collier's British History' could not be obtained. This is more
than answered by the ' i'lpoclis of English History,' They pro
ceed on the liasis on which history should be taught. Divisions are
made according to the inception and cessation of those forces that
brought about changes in the English Constitution, while principles
are clearly communicated and systematized. Not beyond the capa
bilities of younger children, they are also adapted for use in higher
classes.''
BOBT, RoLGERS, Inspcctor of Public Schools, CoUingwood.
"As an aid to the teacher they are invaluable,''
GuELPH Mebcuhy.
" The style is simple, and adapted to the capacity of cliildren at
■chool."
:i»
BEATTY & CLARE'S BbOKKEEPIHG.
A Treatisb on Simolband Double Entry DookKeepino,for usb
IN High and Public Schools. ,
By S. G. Beatty, Principal Ontario Commercial Collepe, BellevMe,and
Samuel Clare, BookKeeping and Writing Master,
Normal School, Toronto.
3rd Ed., PRICE,
70 CENTS.
Authorized by the Minister of Education, Ontario.
Authorized by the Chief Supt. Education, Manitoba.
Beoommended by the Council ofFublio Instr^iction, Quehee.
FROM NOVA SCOTIA AND MANITOBA.
A. C. A. DOANE, Insp. P. Schools, Shelburne Co., Nova Scotia.
" I have carefully looked over Beatty & Clare's Bookkeeping, and
cannot but .u.mire the simplicity of the outline, the oractical bearing of
the transactions, the perspicuity of the instructions, and the varied com
mercial character of the whole work. It commends itself to teachers as
a text book and to all others desirous of acquiring a knowledge of this
important branch."
J. D. McGILLIVRAY, Insp. Schools, Co. Hants., Nova Scotia.
Beaty & Clare's Bookkeeping.— " Besides looking over this book
myself, I have submitted it to the inspection of practical bookkeepers who
agree with me in the propriety of recommending it as a school book.
Its directions are minute and to the point, and its examples ample."
C. T. ANDREWS, Inspector for Queen's Co., Nova S:otia.
"Beatty & Clare's Bookkeepinq has had a careful perusal,
with which the principles of bookkeeping are explained and illustrated,
vvill recommend this work to any teacher or pupil preparing for examina
tion, while it is sufficiently comprehensive for all practical purposes.
L. S. MORSE, M.A., Insp. Schools, Annapolis Co., Nova Scotia.
" I have examined Beatty & Clare's Bookkeeping anrt lind it to be an
excellent v.'ork. The definitions, forms, and transactvjns therein con
tained, are plain and simple, yet comprehensive and ^iractical. It is well
adapted for use in the public schools."
D. H. SMITH, A.M., Insp. Schools, Colchester
" Beatty & Clare's Bookkeeping is an admirabl'
alone is sufficient to secure for the book a place in ou;
the Dominion."
ova Scotia.
's simplicity
. roughout
W. S. DANAGH, Inspector for Cnmberland, N. S.
a I have looked into Beatty & Clare's Bookkeeping, and have much
pleasure in saying that the work is just what is wanted for boys who desire
to acquire in a short time such knowledge as will fit them for business*"
REV. JOHN AMBROSE, M.A., Supt. of Schools, Digby, N. S.
" I am very much pleased with the simplicity and thoroughhess of
Beatty & Clare's Bookkeeping.
THOS. HART, M.A., Winnipeg. ^
«* Several months ago we introduced Mason's English Grammar into
Manitoba College, and now we are introducing Beatty & Clare's Book
keeping. We find them jutt what we oced in their respective subjects."
m
i
A Drill Book for Corrbct and Expressive Kkaoino, Adaptbd
KOR THK USB OP Schools,
By Richard Lewis, Teacher of Elocution, Author of " Dominion Elocu
tionist," &c. 3rd Ed., Price 75 Cents. m^
Authorized by the Minister of Education frr Ontario. Kj
Authorized by the Chief Supt. of Education, Manitoba.
I>. H. SMITH, A.M., Inspector of Schools, Colcboster Co., N. 8.
" Lewis' ' flovr to Bead,' comes In good time. In no branch of
■tndy Is there more deficiency displayed than in that of reading.
Many of our teachers really appear to have no conception as to
how reading ahoiild be taught, but by a careful study of Lewis'
'How to liead' they can without any difllculty render themselves
fit to give instruction with the utmost satisfaction."
L. 8. MOKSE, M.A., Inspector Schools, Annapolis Co., N. S.
"Lewis' 'TIow to Read ' treats of a subject which cannot be too
highly recommended. Such a work is much needed in our sciiools.
The art of rending effectively has been acquired by few teachers,
hence they should pruoure this work and thoroughly and practi
cally master the rules and principles therein contained.
J. D. McGILLlVEAY, Inspeo*;or of Schools, Co. Hants.
 "Lewis' 'ITow to Read,' is the best drill book in elocution for
school use that I have seen. I have road it over with a great deal
of owe."
C. T. ANDREWS, Inspector for Queen's Co., N. S.
"I have examined 'How to lload,' and have no hesitation in
pronouncing it the best little work on elocution for teachers that
hasyetcomo in uler my notice. A thorough drill in the exercises,
with due attention to the elementary sounds of the language as
illustrated by the author, and an intelligent conception of the
principles and suggestions therein given will insure pleasing and
expressive reading. It cannot but be hailed with pleasure by every
teacher as it Bupplies a want long felt in our schools, and gives to
the important Bubjecb of reading its due prominence, as both an
art and a science."
A. C. A. DOANE, Inspector of Schools, Bhelbnme Co., N. S.
" How to Read,' is just what is needed, both as a school class
book and an uid to teachers in the proper training of pupils in the
principles of effective reading.
Rev. JOHN AMBROSE, II.A., Inspector P. Schools, Dlgby, N. S.
How TO Read by Richard Le wis.— " This book, for the size of
it, is the best by far that I have euer seen on the subject."
W. L. DANAGH, Inspector for Cumberland, N. S.
"How to Road is a seasonable publication. As a drill book for
expressive reading it supplies a desideratum in our schools. It
must be admitted that bettov teaching on this branch is greatly
needed. The work shows skill and is highly creditable to the
author."
JOHN Y. GtllM, Broad Cove, Cape Breton, N. S.
" The plan pursued in the arrangements of the work, commen
cing with elements essential to correct vocalization, and leading
cradually on to principles and practice in some of the piuest gems
of the language, must command itself to every admirer of clear,
expressive English reading. The tyrographical ' got up ' of the work
is highly creditable to the enterprising iJublishers.
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I CANADA SCHOOL JOURNAl
Recommended by the Minister of Education in Ontario,
Itecemniendcd by the Boord of Education for Quebec,
liecommended by the iiupt. of Education, 'New JJrunawicle.
"An oxcelleat publication."— Pacific School Journal, Sanfrancisrj.
" The Canada School Journal, puhlisliocl by Adam Miller & Co., Toroi
is a live educutiouul journal, uud should be in the baudB of every teac))
—titratfoid Weekly Herald.
EDITORIAL COMMITTEE.
J. A. MoLoUan, M.A., LL.D., HiRh School Inspector.
Thomaa Kirkland, M.A., Scioiipo Mastor, Normal School.
James Hughes, I'ublic School InB])octor, Toronto.
Alfred Baker, B.A., Math. Tutor. University College, Toronti
PROVINCIAL EDITORS.
Ontario— J. M. Buchan, M.A., High School Inspector.
G. W. Ross, M.P., Tublic School Inspector.
J. C. Glashan, Public School Inspector.
Quebec— W. Dale, M.A., Rector High School.
S. P. Robins, M.A , Supt. Protestant School, Montreal.
New Brunswick— J. Bennett, Ph.D., Supt. City School, Montreal.
Nova Scotia— T. C Simunichrast, Registrar, University of Halifax
Manitoba— John Canioron, B.A., Winnipeg.
British Columbia— John Jessop, Supt. of Fdiication.
CONTRIBUTORS.
Rev. Fi. Ryerson, D.D., J.L.D., late Chief Supt. of Education.
J. G. Hodgins, LL.D., Deputy Minister of Education.
Theodore Rand, A.M., D.C.L., Supt. Education, New Brunswick.
W. Crocket, A.M., Principal Normal School, Fredericton, N.B. ,
J. B. Calkin, M.A., Principal Normal School, Trujro, N.S.
Dr, Baynw, Halifax High School.
Robert Potts, M.A., Cambridge, Eng.
Daniel Wilson, LL.D., I'rof. of History and Eng. Lit., Univ. Coll., L
Rev. S. S. Nelles, D.D., LL.D., Pros. University Victoria College.
Rev. H. G. INIaddock, M.A., F.G.S., Fellow of Clare College, Cambridge,
fessor of Classics, Trinity College, Toionto.
M. Mo Vicar, Ph.D., LL.D,, Principal State Normal and Training Sch
Potsdam, N. Y.
Rev. A. F. Kemp, LL.D., Principal Brantford Young Ladies' Ci j
Geo. Dickson, B.A., Collegiate Institute, Hamilton.
Prof. John A. Macouu, Albert College, Belleville.
Rev. Prof. G. M. Meacham, M.A., Numadza, Japan.
Wm. Johnson, M.A., Principal Agricultural College, Guelph.
John C. McCabe, M.A., Principal Normal School, Ottawa.
Dr. S. P. May, Secretary Centennial Education Committee.
Prof. J. E. Wells, Canadian Literary Institute, Woodstock. . ;
Rev. J. J. Hare, B.A., Ontario Ladies' College, Whitby. ^
James Carlyle, M.D., Math. Master Normal School, To: >ntQ
Geo. Baptie, M.D., Science Master Normal School, Ottawa. f
R. Lewis, Teacher of Elocution, Toronto. >
Prof. R. Bawson. Belleville.
J J. Tilley, Inspector Public Schools, Durham.
CANADA SCHOOL JOURNAL
IS issued Ist of each month from tho Ofhce of Publication, 11 Welling
Street West, Toronto.
Subscription i»l per year, payable in advance.
ADAM MILLER & CO.,
Publishers, Toroii;
:
JOURNAl
ation in Ontario.
■on for Quebec.
m, New Brunswick.
Journal, Sanfrancisrc.
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ito.
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School, Montreal,
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ation.
IS.
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ation.
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•edericton, N.B. ,
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ig. Lit., Univ. Coll., L
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xre College, Cambridge, £
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lool. To: vnta
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rOURNAL
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